Download or read book Jacobians of Plane Quintic Curves of Genus One PHD written by Fahd M. Al-Shammari and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Curves and Their Jacobians written by David Mumford and published by Ann Arbor : University of Michigan Press, c1975, 1976 printing.. This book was released on 1975 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Projective Geometry of Curves of Genus One and an Algorithm for the Jacobian of Such a Curve PHD written by Alexander R. Perlis and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Forms of Plane Quintic Curves written by Linnaeus Wayland Dowling and published by . This book was released on 1897 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Inverse Jacobian and Related Topics for Certain Superelliptic Curves written by Anna Somoza Henares and published by . This book was released on 2019 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given an elliptic curve E over the complex numbers (CC) given by ŷ2 = x̂3 + ax + b, there exists a lattice L in CC such that the group E(CC) of complex points on E is isomorphic to the complex analytic group CC/L. This correspondence between elliptic curves and one-dimensional complex tori is called the Uniformization Theorem, and one can make the inverse map explicit with the Weierstrass p-function, its derivative, and the Eisenstein series. Similarly, given an algebraic curve C of genus g, one associates to it a principally polarized abelian variety J(C), the Jacobian of C. Over CC, the Jacobian J(C) is isomorphic to a g-dimensional complex torus CĈg/L for a lattice L of full rank in CĈg. This determines a map J from the set M_g of isomorphism classes of algebraic curves of genus g to the set A_g of principally polarized abelian varieties of dimension g, and one may wonder if there exists an explicit inverse to this map, as in the case of elliptic curves. We call this the inverse Jacobian problem. This problem has been solved for curves of genus 2 and genus 3. However, for genus g > 3 there is the additional obstruction that not all principally polarized abelian varieties are Jacobians of curves, hence in order to solve the inverse Jacobian problem one needs to study the image by J of M_g in A_g. The problem of describing J(M_g) is known as the Riemann-Schottky problem. In this thesis we treat these two problems for two families of superelliptic curves, that is, curves of the form ŷk = (x - a_1)·...·(x - a_l). We focus on the family of Picard curves, with (k,l) = (3,4) and genus 3, where we give a more efficient solution, and the family of cyclic plane quintic curves, with (k,l) = (5,5) and genus 6, where we solve both problems. We solve the inverse Jacobian problem from a computational point of view, that is, we provide an algorithm to obtain a model for the curve from the lattice L of its Jacobian. While Picard curves have genus 3, hence there is no obstruction to the inverse Jacobian problem, in the case of CPQ curves we also provide a characterization of the principally polarized abelian varieties that arise as Jacobians of CPQ curves. In Chapter 1 we first introduce some background on abelian varieties, Jacobians of curves, and Riemann theta constants, and then we present an inverse Jacobian algorithm for Picard curves. This was originally done by Koike and Weng in their paper "Construction of CM Picard curves", but their exposition presents some mistakes that we address and correct here. This chapter is based on joint work with Joan-Carles Lario. In Chapter 2 we present an inverse Jacobian algorithm for CPQ curves. We follow a strategy analogous to the one in Chapter 1 for the case of Picard curves. In Chapter 3 we address the Riemann-Schottky problem for CPQ curves, that is, we characterize the principally polarized abelian varieties that are Jacobians of CPQ curves. We use a generalization of the classical theory of complex multiplication due to Shimura (see his paper "On analytic families of polarized abelian varieties and automorphic functions") to study how the existence of the automorphism of CPQ curves (x,y) -> (x,ê(2·pi·i/5)y) affects the structure of the Jacobians. Finally, in Chapter 4 we present one application for the above algorithms: constructing curves such that their Jacobians have complex multiplication. This has previously been done for genus 2 and genus 3, and here we follow methods presented by Kilicer in her PhD thesis to determine a complete list of CM-fields whose ring of integers occurs as the endomorphism ring over CC of the Jacobian of a CPQ curve defined over the rational numbers. In particular, for every field K listed in Chapter 4 we also give a CPQ curve that is numerically close (and conjecturally equal) to a curve C that satisfies End(J(CC)) = O_K.

Download or read book On Plane Quintic Curves written by Hermon Lester Slobin and published by . This book was released on 1908 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Celebration of Algebraic Geometry written by Brendan Hassett and published by American Mathematical Soc.. This book was released on 2013-09-11 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Download or read book Computations in Algebraic Geometry with Macaulay 2 written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Download or read book Rational Algebraic Curves written by J. Rafael Sendra and published by Springer Science & Business Media. This book was released on 2007-12-10 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.

Download or read book Solving Systems of Polynomial Equations written by Bernd Sturmfels and published by American Mathematical Soc.. This book was released on 2002 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging a number of mathematical disciplines, and exposing many facets of systems of polynomial equations, Bernd Sturmfels's study covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.

Download or read book The 1 2 3 of Modular Forms written by Jan Hendrik Bruinier and published by Springer Science & Business Media. This book was released on 2008-02-10 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.

Download or read book Rational Points on Varieties written by Bjorn Poonen and published by American Mathematical Soc.. This book was released on 2017-12-13 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere.

Download or read book The Restricted Three Body Problem and Holomorphic Curves written by Urs Frauenfelder and published by Springer. This book was released on 2018-08-29 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019

Download or read book Pioneering Women in American Mathematics written by Judy Green and published by American Mathematical Soc.. This book was released on 2009 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is the result of a study in which the authors identified all of the American women who earned PhD's in mathematics before 1940, and collected extensive biographical and bibliographical information about each of them. By reconstructing as complete a picture as possible of this group of women, Green and LaDuke reveal insights into the larger scientific and cultural communities in which they lived and worked." "The book contains an extended introductory essay, as well as biographical entries for each of the 228 women in the study. The authors examine family backgrounds, education, careers, and other professional activities. They show that there were many more women earning PhD's in mathematics before 1940 than is commonly thought." "The material will be of interest to researchers, teachers, and students in mathematics, history of mathematics, history of science, women's studies, and sociology."--BOOK JACKET.

Download or read book Rational Points on Algebraic Varieties written by Emmanuel Peyre and published by Birkhäuser. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of rational and integral points on higher-dimensional algebraic varieties. It contains carefully selected research papers addressing the arithmetic geometry of varieties which are not of general type, with an emphasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The present volume gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric constructions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups.

Download or read book Poisson Structures written by Camille Laurent-Gengoux and published by Springer Science & Business Media. This book was released on 2012-08-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.​