Download or read book Positivity in Algebraic Geometry I written by R.K. Lazarsfeld and published by Springer Science & Business Media. This book was released on 2004-08-24 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Volume I is more elementary than Volume II, and, for the most part, it can be read without access to Volume II.
Download or read book Positivity in Algebraic Geometry II written by R.K. Lazarsfeld and published by Springer. This book was released on 2017-07-25 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two volume work containing a contemporary account on "Positivity in Algebraic Geometry". Both volumes also available as hardcover editions as Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete". A good deal of the material has not previously appeared in book form. Volume II is more at the research level and somewhat more specialized than Volume I. Volume II contains a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. Contains many concrete examples, applications, and pointers to further developments
Download or read book Positivity in Algebraic Geometry written by and published by . This book was released on 2004 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Positivity in Algebraic Geometry written by Robert Lazarsfeld and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Positivity in algebraic geometry written by Robert Lazarsfeld and published by . This book was released on 2011-04-13 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Positivity in Algebraic Geometry I Classical Setting Line Bundles and Linear Series written by Robert Lazarsfeld and published by . This book was released on 2004 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Positive Polynomials written by Alexander Prestel and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Positivity is one of the most basic mathematical concepts, involved in many areas of mathematics (analysis, real algebraic geometry, functional analysis, etc.). The main objective of the book is to give useful characterizations of polynomials. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed.
Download or read book Recent Advances in Algebraic Geometry written by Christopher D. Hacon and published by Cambridge University Press. This book was released on 2015-01-15 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.
Download or read book Emerging Applications of Algebraic Geometry written by Mihai Putinar and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.
Download or read book Certificates of Positivity for Real Polynomials written by Victoria Powers and published by Springer Nature. This book was released on 2021-11-26 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects and explains the many theorems concerning the existence of certificates of positivity for polynomials that are positive globally or on semialgebraic sets. A certificate of positivity for a real polynomial is an algebraic identity that gives an immediate proof of a positivity condition for the polynomial. Certificates of positivity have their roots in fundamental work of David Hilbert from the late 19th century on positive polynomials and sums of squares. Because of the numerous applications of certificates of positivity in mathematics, applied mathematics, engineering, and other fields, it is desirable to have methods for finding, describing, and characterizing them. For many of the topics covered in this book, appropriate algorithms, computational methods, and applications are discussed. This volume contains a comprehensive, accessible, up-to-date treatment of certificates of positivity, written by an expert in the field. It provides an overview of both the theory and computational aspects of the subject, and includes many of the recent and exciting developments in the area. Background information is given so that beginning graduate students and researchers who are not specialists can learn about this fascinating subject. Furthermore, researchers who work on certificates of positivity or use them in applications will find this a useful reference for their work.
Download or read book Notions of Positivity and the Geometry of Polynomials written by Petter Brändén and published by Springer Science & Business Media. This book was released on 2011-09-01 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of solicited articles from a select group of mathematicians and physicists working at the interface between positivity and the geometry, combinatorics or analysis of polynomials of one or several variables. It is dedicated to the memory of Julius Borcea (1968-2009), a distinguished mathematician, Professor at the University of Stockholm. With his extremely original contributions and broad vision, his impact on the topics of the planned volume cannot be underestimated. All contributors knew or have exchanged ideas with Dr. Borcea, and their articles reflect, at least partially, his heritage.
Download or read book Enumerative Geometry and Classical Algebraic Geometry written by Lebarz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ce. volume. u.t fioJtme de. la Ve. M-ion de6~ve. du .te.x.tu du cOn6Vte.n.cV6 fia-i.tu a N-ice. au cowu., d' un CoUoque. qu-i f.>' Ij u.t .te.n.u du 23 au 27 Ju-in 1981. Comme. Ie. f.>ugge. ILe. Mn ~e., Ie. f.>uje.t, volon.t~e.me.n.t ILU.tfLe.-in.t, gfLav-i.ta-i.t gILof.>f.>o-modo au.toulL du upacu pILoje.c.t-i6f.> de. pe.t-i.te. d-ime.n f.>-ion e.t du co UfLbe.f.>, ce.la f.>UfL un COfLpf.> aigebfL-ique.me.n.t elM. Ii f.>e.mble. que. ce. cho-ix deUbVte a-i.t Ue b-ie.n accu~ danf.> I' e.nf.>e.mble. pM lu pa. Jt:ttupan.tf.>. Le. Colloque. a IL(LMe.mble une. M-ixan.ta-in.e. de. f.>peu~.tu ve.n.uf.> de. d-i66eILe.n.tf.> paljf.> e.t nouf.> noUf.> f.>ommu e.n pa. Jt:ttcuUe.fL ILejo~ de. l'-im pofL.tan.te. pa. Jt:ttc-ipatio n de. nof.> vo~-inf.> -i.taUe.nf.>. Le. pIL06Uf.>e. UfL VIEuVONNE n'aljaYt.t paf.> pu pa. Jt:ttupe.fL au colloque.
Download or read book Intersection Theory written by W. Fulton and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the ancient origins of algebraic geometry in the solution of polynomial equations, through the triumphs of algebraic geometry during the last two cen turies, intersection theory has played a central role. Since its role in founda tional crises has been no less prominent, the lack of a complete modern treatise on intersection theory has been something of an embarrassment. The aim of this book is to develop the foundations of intersection theory, and to indicate the range of classical and modern applications. Although a comprehensive his tory of this vast subject is not attempted, we have tried to point out some of the striking early appearances of the ideas of intersection theory. Recent improvements in our understanding not only yield a stronger and more useful theory than previously available, but also make it possible to devel op the subject from the beginning with fewer prerequisites from algebra and algebraic geometry. It is hoped that the basic text can be read by one equipped with a first course in algebraic geometry, with occasional use of the two appen dices. Some of the examples, and a few of the later sections, require more spe cialized knowledge. The text is designed so that one who understands the con structions and grants the main theorems of the first six chapters can read other chapters separately. Frequent parenthetical references to previous sections are included for such readers. The summaries which begin each chapter should fa cilitate use as a reference.
Download or read book Semidefinite Optimization and Convex Algebraic Geometry written by Grigoriy Blekherman and published by SIAM. This book was released on 2013-03-21 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Download or read book A Course in Real Algebraic Geometry written by Claus Scheiderer and published by Springer. This book was released on 2024-10-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for a one-year graduate course in real algebraic geometry, with a particular focus on positivity and sums of squares of polynomials. The first half of the book features a thorough introduction to ordered fields and real closed fields, including the Tarski–Seidenberg projection theorem and transfer principle. Classical results such as Artin's solution to Hilbert's 17th problem and Hilbert's theorems on sums of squares of polynomials are presented in detail. Other features include careful introductions to the real spectrum and to the geometry of semialgebraic sets. The second part studies Archimedean positivstellensätze in great detail and in various settings, together with important applications. The techniques and results presented here are fundamental to contemporary approaches to polynomial optimization. Important results on sums of squares on projective varieties are covered as well. The last part highlights applications to semidefinite programming and polynomial optimization, including recent research on semidefinite representation of convex sets. Written by a leading expert and based on courses taught for several years, the book assumes familiarity with the basics of commutative algebra and algebraic varieties, as can be covered in a one-semester first course. Over 350 exercises, of all levels of difficulty, are included in the book.
Download or read book Algebraic Geometry II written by David Mumford and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several generations of students of algebraic geometry have learned the subject from David Mumford's fabled "Red Book" containing notes of his lectures at Harvard University. This book contains what Mumford had intended to be Volume II. It covers the material in the "Red Book" in more depth with several more topics added.
Download or read book Birational Geometry of Algebraic Varieties written by Janos Kollár and published by Cambridge University Press. This book was released on 2010-03-24 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.
