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Cox Rings

Cox Rings Author Ivan Arzhantsev
ISBN-10 9781316147955
Release 2014-08-29
Pages
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Cox rings are significant global invariants of algebraic varieties, naturally generalizing homogeneous coordinate rings of projective spaces. This book provides a largely self-contained introduction to Cox rings, with a particular focus on concrete aspects of the theory. Besides the rigorous presentation of the basic concepts, other central topics include the case of finitely generated Cox rings and its relation to toric geometry; various classes of varieties with group actions; the surface case; and applications in arithmetic problems, in particular Manin's conjecture. The introductory chapters require only basic knowledge in algebraic geometry. The more advanced chapters also touch on algebraic groups, surface theory, and arithmetic geometry. Each chapter ends with exercises and problems. These comprise mini-tutorials and examples complementing the text, guided exercises for topics not discussed in the text, and, finally, several open problems of varying difficulty.



Combinatorial Algebraic Geometry

Combinatorial Algebraic Geometry Author Gregory G. Smith
ISBN-10 9781493974863
Release 2017-11-17
Pages 390
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This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.



Singularities of the Minimal Model Program

Singularities of the Minimal Model Program Author János Kollár
ISBN-10 9781107311473
Release 2013-02-21
Pages
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This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.



Algebraic Theory of Locally Nilpotent Derivations

Algebraic Theory of Locally Nilpotent Derivations Author Gene Freudenburg
ISBN-10 9783662553503
Release 2017-09-08
Pages 319
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This book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as commutative algebra, representation theory, Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane and the Cancellation Theorem for Curves. More recent results, such as Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings, are also discussed. Topics of special interest include progress in classifying additive actions on three-dimensional affine space, finiteness questions (Hilbert's 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. A lot of new material is included in this expanded second edition, such as canonical factorization of quotient morphisms, and a more extended treatment of linear actions. The reader will also find a wealth of examples and open problems and an updated resource for future investigations.



Galois Theories

Galois Theories Author Francis Borceux
ISBN-10 0521803098
Release 2001-02-22
Pages 341
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Develops Galois theory in a more general context, emphasizing category theory.



Erdos Ko Rado Theorems Algebraic Approaches

Erdos Ko Rado Theorems  Algebraic Approaches Author
ISBN-10 9781107128446
Release
Pages
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Erdos Ko Rado Theorems Algebraic Approaches has been writing in one form or another for most of life. You can find so many inspiration from Erdos Ko Rado Theorems Algebraic Approaches also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Erdos Ko Rado Theorems Algebraic Approaches book for free.



Lectures on Lyapunov Exponents

Lectures on Lyapunov Exponents Author Marcelo Viana
ISBN-10 9781107081734
Release 2014-07-24
Pages 215
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The theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the subject to dynamical systems, ergodic theory, mathematical physics and probability. It is based on the author's own graduate course and is reasonably self-contained with an extensive set of exercises provided at the end of each chapter. This book makes a welcome addition to the literature, serving as a graduate text and a valuable reference for researchers in the field.



Unit Equations in Diophantine Number Theory

Unit Equations in Diophantine Number Theory Author Jan-Hendrik Evertse
ISBN-10 9781107097605
Release 2015-10-31
Pages 384
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Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.



Commutative Ring Theory

Commutative Ring Theory Author H. Matsumura
ISBN-10 0521367646
Release 1989-05-25
Pages 320
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This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.



Annales Scientifiques de L cole Normale Sup rieure

Annales Scientifiques de L   cole Normale Sup  rieure Author
ISBN-10 UOM:39015072629259
Release 2007
Pages
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Annales Scientifiques de L cole Normale Sup rieure has been writing in one form or another for most of life. You can find so many inspiration from Annales Scientifiques de L cole Normale Sup rieure also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Annales Scientifiques de L cole Normale Sup rieure book for free.



Algebra Number Theory

Algebra   Number Theory Author
ISBN-10 UCSD:31822036938454
Release 2008
Pages
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Algebra Number Theory has been writing in one form or another for most of life. You can find so many inspiration from Algebra Number Theory also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Algebra Number Theory book for free.



Combinatorial Commutative Algebra

Combinatorial Commutative Algebra Author Ezra Miller
ISBN-10 9780387271033
Release 2006-03-30
Pages 420
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Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs



Algebraic Number Theory

Algebraic Number Theory Author Jürgen Neukirch
ISBN-10 9783662039830
Release 2013-03-14
Pages 574
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This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples. It is the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.



Official Gazette

Official Gazette Author
ISBN-10 WISC:89119246379
Release 2011
Pages
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Official Gazette has been writing in one form or another for most of life. You can find so many inspiration from Official Gazette also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Official Gazette book for free.



Arithmetic of Higher Dimensional Algebraic Varieties

Arithmetic of Higher Dimensional Algebraic Varieties Author Bjorn Poonen
ISBN-10 081763259X
Release 2004
Pages 287
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One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings. It has become clear that the study of rational and integral points has deep connections to other branches of mathematics: complex algebraic geometry, Galois and étale cohomology, transcendence theory and diophantine approximation, harmonic analysis, automorphic forms, and analytic number theory. This text, which focuses on higher-dimensional varieties, provides precisely such an interdisciplinary view of the subject. It is a digest of research and survey papers by leading specialists; the book documents current knowledge in higher-dimensional arithmetic and gives indications for future research. It will be valuable not only to practitioners in the field, but to a wide audience of mathematicians and graduate students with an interest in arithmetic geometry. Contributors: Batyrev, V.V.; Broberg, N.; Colliot-Thélène, J-L.; Ellenberg, J.S.; Gille, P.; Graber, T.; Harari, D.; Harris, J.; Hassett, B.; Heath-Brown, R.; Mazur, B.; Peyre, E.; Poonen, B.; Popov, O.N.; Raskind, W.; Salberger, P.; Scharaschkin, V.; Shalika, J.; Starr, J.; Swinnerton-Dyer, P.; Takloo-Bighash, R.; Tschinkel, Y.: Voloch, J.F.; Wittenberg, O.



Introduction to Algebraic Geometry

Introduction to Algebraic Geometry Author Brendan Hassett
ISBN-10 9781139464598
Release 2007-05-03
Pages
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Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.



Gr bner Bases and Convex Polytopes

Gr  bner Bases and Convex Polytopes Author Bernd Sturmfels
ISBN-10 9780821804872
Release 1996
Pages 162
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This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Grobner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.