Download or read book Lefschetz Properties written by Uwe Nagel and published by Springer Nature. This book was released on with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Lefschetz Properties written by Tadahito Harima and published by Springer. This book was released on 2013-08-23 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph which collects basic techniques, major results and interesting applications of Lefschetz properties of Artinian algebras. The origin of the Lefschetz properties of Artinian algebras is the Hard Lefschetz Theorem, which is a major result in algebraic geometry. However, for the last two decades, numerous applications of the Lefschetz properties to other areas of mathematics have been found, as a result of which the theory of the Lefschetz properties is now of great interest in its own right. It also has ties to other areas, including combinatorics, algebraic geometry, algebraic topology, commutative algebra and representation theory. The connections between the Lefschetz property and other areas of mathematics are not only diverse, but sometimes quite surprising, e.g. its ties to the Schur-Weyl duality. This is the first book solely devoted to the Lefschetz properties and is the first attempt to treat those properties systematically.
Download or read book Deformation of Artinian Algebras and Jordan Type written by Anthony Iarrobino and published by American Mathematical Society. This book was released on 2024-09-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS-EMS-SMF Special Session on Deformations of Artinian Algebras and Jordan Type, held July 18?22, 2022, at the Universit‚ Grenoble Alpes, Grenoble, France. Articles included are a survey and open problems on deformations and relation to the Hilbert scheme; a survey of commuting nilpotent matrices and their Jordan type; and a survey of Specht ideals and their perfection in the two-rowed case. Other articles treat topics such as the Jordan type of local Artinian algebras, Waring decompositions of ternary forms, questions about Hessians, a geometric approach to Lefschetz properties, deformations of codimension two local Artin rings using Hilbert-Burch matrices, and parametrization of local Artinian algebras in codimension three. Each of the articles brings new results on the boundary of commutative algebra and algebraic geometry.
Download or read book Rational Points Rational Curves and Entire Holomorphic Curves on Projective Varieties written by Carlo Gasbarri and published by American Mathematical Soc.. This book was released on 2015-12-22 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers from the Short Thematic Program on Rational Points, Rational Curves, and Entire Holomorphic Curves and Algebraic Varieties, held from June 3-28, 2013, at the Centre de Recherches Mathématiques, Université de Montréal, Québec, Canada. The program was dedicated to the study of subtle interconnections between geometric and arithmetic properties of higher-dimensional algebraic varieties. The main areas of the program were, among others, proving density of rational points in Zariski or analytic topology on special varieties, understanding global geometric properties of rationally connected varieties, as well as connections between geometry and algebraic dynamics exploring new geometric techniques in Diophantine approximation. This book is co-published with the Centre de Recherches Mathématiques.
Download or read book Surveys in Combinatorics 2021 written by Konrad K. Dabrowski and published by Cambridge University Press. This book was released on 2021-06-24 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains nine survey articles based on plenary lectures given at the 28th British Combinatorial Conference, hosted online by Durham University in July 2021. This biennial conference is a well-established international event, attracting speakers from around the world. Written by some of the foremost researchers in the field, these surveys provide up-to-date overviews of several areas of contemporary interest in combinatorics. Topics discussed include maximal subgroups of finite simple groups, Hasse–Weil type theorems and relevant classes of polynomial functions, the partition complex, the graph isomorphism problem, and Borel combinatorics. Representing a snapshot of current developments in combinatorics, this book will be of interest to researchers and graduate students in mathematics and theoretical computer science.
Download or read book Commutative Algebra written by Irena Peeva and published by Springer Science & Business Media. This book was released on 2013-02-01 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.
Download or read book Gr bner s Problem and the Geometry of GT Varieties written by Liena Colarte-Gómez and published by Springer Nature. This book was released on with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Geometry of Some Special Projective Varieties written by Francesco Russo and published by Springer. This book was released on 2016-01-25 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorne’s Conjecture on Complete Intersections for the class of quadratic manifolds and new short proofs of previously known results, using the modern tools of Mori Theory and of rationally connected manifolds. The new approach to some of the problems considered can be resumed in the principle that, instead of studying a special embedded manifold uniruled by lines, one passes to analyze the original geometrical property on the manifold of lines passing through a general point and contained in the manifold. Once this embedded manifold, usually of lower codimension, is classified, one tries to reconstruct the original manifold, following a principle appearing also in other areas of geometry such as projective differential geometry or complex geometry.
Download or read book Noncommutative Geometry Quantum Fields and Motives written by Alain Connes and published by American Mathematical Soc.. This book was released on 2019-03-13 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
Download or read book Power Sums Gorenstein Algebras and Determinantal Loci written by Anthony Iarrobino and published by Springer Science & Business Media. This book was released on 1999-12-15 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the theory of representations of homogeneous polynomials as sums of powers of linear forms. The first two chapters are introductory, and focus on binary forms and Waring's problem. Then the author's recent work is presented mainly on the representation of forms in three or more variables as sums of powers of relatively few linear forms. The methods used are drawn from seemingly unrelated areas of commutative algebra and algebraic geometry, including the theories of determinantal varieties, of classifying spaces of Gorenstein-Artin algebras, and of Hilbert schemes of zero-dimensional subschemes. Of the many concrete examples given, some are calculated with the aid of the computer algebra program "Macaulay", illustrating the abstract material. The final chapter considers open problems. This book will be of interest to graduate students, beginning researchers, and seasoned specialists. Prerequisite is a basic knowledge of commutative algebra and algebraic geometry.
Download or read book Issues in Algebra Geometry and Topology 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Algebra, Geometry, and Topology / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Topology. The editors have built Issues in Algebra, Geometry, and Topology: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Topology in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Algebra, Geometry, and Topology: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Download or read book Homotopy Methods in Topological Fixed and Periodic Points Theory written by Jerzy Jezierski and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of a ?xed point plays a crucial role in numerous branches of mat- maticsand its applications. Informationabout the existence of such pointsis often the crucial argument in solving a problem. In particular, topological methods of ?xed point theory have been an increasing focus of interest over the last century. These topological methods of ?xed point theory are divided, roughly speaking, into two types. The ?rst type includes such as the Banach Contraction Principle where the assumptions on the space can be very mild but a small change of the map can remove the ?xed point. The second type, on the other hand, such as the Brouwer and Lefschetz Fixed Point Theorems, give the existence of a ?xed point not only for a given map but also for any its deformations. This book is an exposition of a part of the topological ?xed and periodic point theory, of this second type, based on the notions of Lefschetz and Nielsen numbers. Since both notions are homotopyinvariants, the deformationis used as an essential method, and the assertions of theorems typically state the existence of ?xed or periodic points for every map of the whole homotopy class, we refer to them as homotopy methods of the topological ?xed and periodic point theory.
Download or read book Tropical Geometry and Integrable Systems written by Chris Athorne and published by American Mathematical Soc.. This book was released on 2012 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on tropical geometry and integrable systems, held July 3-8, 2011, at the University of Glasgow, United Kingdom. One of the aims of this conference was to bring together researchers in the field of tropical geometry and its applications, from apparently disparate ends of the spectrum, to foster a mutual understanding and establish a common language which will encourage further developments of the area. This aim is reflected in these articles, which cover areas from automata, through cluster algebras, to enumerative geometry. In addition, two survey articles are included which introduce ideas from researchers on one end of this spectrum to researchers on the other. This book is intended for graduate students and researchers interested in tropical geometry and integrable systems and the developing links between these two areas.
Download or read book Algebraic Models in Geometry written by Yves Félix and published by Oxford University Press. This book was released on 2008 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: A text aimed at both geometers needing the tools of rational homotopy theory to understand and discover new results concerning various geometric subjects, and topologists who require greater breadth of knowledge about geometric applications of the algebra of homotopy theory.
Download or read book Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Boyan Sirakov and published by World Scientific. This book was released on 2019-02-27 with total page 5393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Download or read book On the Shape of a Pure O Sequence written by Mats Boij and published by American Mathematical Soc.. This book was released on 2012 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: A monomial order ideal is a finite collection X of (monic) monomials such that, whenever M∈X and N divides M, then N∈X. Hence X is a poset, where the partial order is given by divisibility. If all, say t t, maximal monomials of X have the same degree, then X is pure (of type t). A pure O-sequence is the vector, h_=(h0=1,h1,...,he), counting the monomials of X in each degree. Equivalently, pure O-sequences can be characterized as the f-vectors of pure multicomplexes, or, in the language of commutative algebra, as the h h-vectors of monomial Artinian level algebras. Pure O-sequences had their origin in one of the early works of Stanley's in this area, and have since played a significant role in at least three different disciplines: the study of simplicial complexes and their f f-vectors, the theory of level algebras, and the theory of matroids. This monograph is intended to be the first systematic study of the theory of pure O-sequences.
Download or read book Featured Reviews in Mathematical Reviews 1997 1999 written by Donald G. Babbitt and published by American Mathematical Soc.. This book was released on 2000-05-05 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.
