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Author: Christopher D. Hacon
Publisher: Cambridge University Press
Published: 2015-01-15
Total Pages: 451
ISBN-13: 110764755X
DOWNLOAD EBOOKA comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.
Author: Izzet Coskun
Publisher: American Mathematical Soc.
Published: 2017-07-12
Total Pages: 386
ISBN-13: 1470435578
DOWNLOAD EBOOKThe algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.
Author: Lucia Caporaso
Publisher: Cambridge University Press
Published: 2012-03-19
Total Pages: 437
ISBN-13: 052176825X
DOWNLOAD EBOOKThis volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.
Author: Christopher D. Hacon
Publisher: Cambridge University Press
Published: 2015-01-15
Total Pages: 451
ISBN-13: 131619583X
DOWNLOAD EBOOKContemporary research in algebraic geometry is the focus of this collection, which presents articles on modern aspects of the subject. The list of topics covered is a roll-call of some of the most important and active themes in this thriving area of mathematics: the reader will find articles on birational geometry, vanishing theorems, complex geometry and Hodge theory, free resolutions and syzygies, derived categories, invariant theory, moduli spaces, and related topics, all written by leading experts. The articles, which have an expository flavour, present an overall picture of current research in algebraic geometry, making this book essential for researchers and graduate students. This volume is the outcome of the conference Recent Advances in Algebraic Geometry, held in Ann Arbor, Michigan, to honour Rob Lazarsfeld's many contributions to the subject on the occasion of his 60th birthday.
Author: Steven Dale Cutkosky
Publisher: American Mathematical Soc.
Published: 2018-06-01
Total Pages: 498
ISBN-13: 1470435187
DOWNLOAD EBOOKThis book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.
Author: Edgar Martinez-moro
Publisher: World Scientific
Published: 2008-10-08
Total Pages: 453
ISBN-13: 9814471615
DOWNLOAD EBOOKAdvances in Algebraic Geometry Codes presents the most successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of a part of the information due to either interferences in the telecommunications or degradation of the information-storing support (for instance, compact disc). An error-correcting code thus adds extra information to the message to be transmitted with the aim of recovering the sent information. With contributions from renowned researchers, this pioneering book will be of value to mathematicians, computer scientists, and engineers in information theory.
Author: Mihai Putinar
Publisher: Springer Science & Business Media
Published: 2008-12-10
Total Pages: 382
ISBN-13: 0387096868
DOWNLOAD EBOOKRecent 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.
Author: Robin Hartshorne
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 511
ISBN-13: 1475738498
DOWNLOAD EBOOKAn introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Author: Matt Kerr
Publisher: Cambridge University Press
Published: 2016-02-04
Total Pages: 533
ISBN-13: 110754629X
DOWNLOAD EBOOKCombines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.
Author: Hal Schenck
Publisher: Cambridge University Press
Published: 2003-10-06
Total Pages: 212
ISBN-13: 9780521536509
DOWNLOAD EBOOKThe interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Advances in computing and algorithms make it possible to tackle many classical problems in a down-to-earth and concrete fashion. This opens wonderful new vistas and allows us to pose, study and solve problems that were previously out of reach. Suitable for graduate students, the objective of this 2003 book is to bring advanced algebra to life with lots of examples. The first chapters provide an introduction to commutative algebra and connections to geometry. The rest of the book focuses on three active areas of contemporary algebra: Homological Algebra (the snake lemma, long exact sequence inhomology, functors and derived functors (Tor and Ext), and double complexes); Algebraic Combinatorics and Algebraic Topology (simplicial complexes and simplicial homology, Stanley-Reisner rings, upper bound theorem and polytopes); and Algebraic Geometry (points and curves in projective space, Riemann-Roch, Cech cohomology, regularity).
