Algebraic

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Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a difficult problem with many applications outside of mathematics. While it is hopeless to expect much in general, we know a surprising amount about...

Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in ""Algebraic Geometry 1: From Algebraic Varieties to Schemes"", (see Volume 185 in the same series, ""Translations of Mathematical...

Algebraic geometry plays an important role in several branches of science and technology. This is the last of three volumes by Kenji Ueno algebraic geometry. This, in together with ""Algebraic Geometry 1"" and ""Algebraic Geometry 2"", makes an excellent...

This book formulates a new conjecture about quadratic periods of automorphic forms on quaternion algebras, which is an integral refinement of Shimura's algebraicity conjectures on these periods. It also provides a strategy to attack this conjecture by...

An accessible, motivated introduction to one of the most dynamic areas of mathematicsDecades ago, Mumford wrote that algebraic geometry "seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are...

This book discusses the connection between Calabi-Yau threefolds and modular forms. It presents the general theory and brings together the known results. Hundreds of new examples are given of rigid and non-rigid Calabi-Yau threefolds, and the...

This open access book is a tribute to the profound contributions of Professor Bumsig Kim in the field of mathematics, particularly in the realm of mirror symmetry. Mirror symmetry is a fascinating duality between complex/algebraic geometry and symplectic...

The need for an axiomatic treatment of homology and cohomology theory has long been felt by topologists. Professors Eilenberg and Steenrod present here for the first time an axiomatization of the complete transition from topology to algebra. Originally...

A guide to the basics of modern algebraic geometry.Book InformationISBN 9780821810293Author American Mathematical SocietyFormat PaperbackPage Count 363Imprint American Mathematical SocietyPublisher American Mathematical SocietyWeight(grams)...

The description for this book, Ramification Theoretic Methods in Algebraic Geometry (AM-43), will be forthcoming.Book InformationISBN 9780691080239Author Shreeram Shankar AbhyankarFormat PaperbackPage Count 112Imprint Princeton University PressPublisher...

The goal of this book is to cover the active developments of arithmetically Cohen-Macaulay and Ulrich bundles and related topics in the last 30 years, and to present relevant techniques and multiple applications of the theory of Ulrich bundles to a wide...

Arising from the 2022 Japan-US Mathematics Institute, this book covers a range of topics in modern algebraic geometry, including birational geometry, classification of varieties in positive and zero characteristic, K-stability, Fano varieties,...

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...

Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject. As a deeper understanding of this analogy...

The study of geometry can play an important role in stimulating mathematical imagination and intuition, particularly in its relation to algebra. The author of this book is convinced that the two are but different sides of the same coin, and that they...

Schubert varieties lie at the cross roads of algebraic geometry, combinatorics, commutative algebra, and representation theory. They are an important class of subvarieties of flag varieties, interesting in their own right, and providing an inductive tool...

MATRIX is Australia's international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record...

MATRIX is Australia's international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record...

This book arose from a conference on "Singularities and Computer Algebra" which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel's 70th birthday. This unique volume presents a collection of recent original research by...

The finite generation theorem is a major achievement in modern algebraic geometry. Based on the minimal model theory, it states that the canonical ring of an algebraic variety defined over a field of characteristic 0 is a finitely generated graded ring...

This book provides a comprehensive and user-friendly exploration of the tremendous recent developments that reveal the connections between real algebraic geometry and optimization, two subjects that were usually taught separately until the beginning of...

This book provides a comprehensive and user-friendly exploration of the tremendous recent developments that reveal the connections between real algebraic geometry and optimization, two subjects that were usually taught separately until the beginning of...

Apologies but we at Booksplease don't have a full description for this book.About the AuthorCheol-Hyun Cho, Seoul National University, Seoul, South Korea.Hansol Hong, Yonsei University, Seoul, Korea.Book InformationISBN 9781470447618Author Cheol-Hyun...

This book features plane curves-the simplest objects in differential geometry-to illustrate many deep and inspiring results in the field in an elementary and accessible way. After an introduction to the basic properties of plane curves, the authors...

Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in other parts of mathematics, most prominently in representation theory. This volume develops deformation theory, Lie theory and the...

This volume contains the proceedings of the Conference on Compactifications, Configurations, and Cohomology, held from October 22-24, 2021, at Northeastern University, Boston, MA. Some of the most active and fruitful mathematical research occurs at the...

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A Concise Introduction to Algebraic Varieties is designed for a one-term introductory course on algebraic varieties over an algebraically closed field, and it provides a solid basis for a course on schemes and cohomology or on specialized topics, such as...

The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become...

It is by now a well-known paradigm that public-key cryptosystems can be built using finite Abelian groups and that algebraic geometry provides a supply of such groups through Abelian varieties over finite fields. Of special interest are the Abelian...

The first application of modern algebraic techniques to a comprehensive selection of classical geometric problems. Written with spirit and originality, this is a valuable book for anyone interested in the subject from other than the purely algebraic...

A pioneering new nonlinear approach to a fundamental question in algebraic geometryOne of the crowning achievements of nineteenth-century mathematics was the proof that the geometry of lines in space uniquely determines the Cartesian coordinates, up to a...

This book presents a new and innovative approach to Lie groups and differential geometry. Rather than compiling and reviewing the existing material on this classical subject, Professor Ortacgil instead questions the foundations of the subject, and...

Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A...

The description for this book, Topics in Transcendental Algebraic Geometry. (AM-106), will be forthcoming.Book InformationISBN 9780691083391Author Phillip A. GriffithsFormat PaperbackPage Count 328Imprint Princeton University PressPublisher Princeton...

The aim of this book is to study various geometric properties and algebraic invariants of smooth projective varieties with infinite fundamental groups. This approach allows for much interplay between methods of algebraic geometry, complex analysis, the...

There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham...

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...

The central theme of this book is the study of self-dual connections on four-manifolds. The authors have adopted a topologists' perspective and so have included many of the explicit calculations using the Atiyah-Singer index theorem as well as presenting...