Algebraic geometry

Projective duality is a very classical notion naturally arising in various areas of mathematics, such as algebraic and differential geometry, combinatorics, topology, analytical mechanics, and invariant theory, and the results in this field were until now scattered across the literature.

This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves.

This book constitutes the proceedings of the 2000 Howard conference on "e;Infinite Dimensional Lie Groups in Geometry and Representation Theory"e;.

This volume consists of 15 papers contributing to the Hayama Symposium on Complex Analysis in Several Variables XXIII, which was dedicated to the 100th anniversary of the creation of the Bergman kernel.

In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume.

The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields.

In 1961 the second author deliv1lred a series of lectures at Haverford Col- lege on the subject of "e;Rational Points on Cubic Curves.

This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces.

The modern theory of Kleinian groups starts with the work of Lars Ahlfors and Lipman Bers; specifically with Ahlfors' finiteness theorem, and Bers' observation that their joint work on the Beltrami equation has deep implications for the theory of Kleinian groups and their deformations.

This proceedings volume contains articles related to the research presented at the 2019 Simons Symposium on p-adic Hodge theory.

This book is based on a series of lectures given by the author at SISSA, Trieste, within the PhD courses Techniques in enumerative geometry (2019) and Localisation in enumerative geometry (2021).

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Computational Geometry is a new discipline of computer science that deals with the design and analysis of algorithms for solving geometric problems.

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The ambitious program for the birational classification of higher-dimensional complex algebraic varieties initiated by Shigeru Iitaka around 1970 is usually called the Iitaka program.

This book is an exposition of recent progress on the Donaldson-Thomas (DT) theory.

This book includes 58 selected articles that highlight the major contributions of Professor Radha Charan Gupta-a doyen of history of mathematics-written on a variety of important topics pertaining to mathematics and astronomy in India.

Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

This book is based on one-semester courses given at Harvard in 1984, at Brown in 1985, and at Harvard in 1988.

This book, one of the first on G2 manifolds in decades, collects introductory lectures and survey articles largely based on talks given at a workshop held at the Fields Institute in August 2017, as part of the major thematic program on geometric analysis.

Since its very existence as a separate field within computerscience, computer graphics had to make extensive use ofnon-trivial mathematics, for example, projective geometry,solid modelling, and approximation theory.

Mumford's famous Red Book gives a simple readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra.

Algebraic curves are the graphs of polynomial equations in two vari- 3 ables, such as y3 + 5xy2 = x + 2xy.

This book summarizes recent inventions, provides guidelines and recommendations, and demonstrates many practical applications of homomorphic encryption.

This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory.

This textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory.

The thoroughly revised and updated second edition of this acclaimed text has several new and expanded sections and more than 1,100 exercises.

This volume collects contributions by leading experts in the area of commutative algebra related to the INdAM meeting "e;Homological and Computational Methods in Commutative Algebra"e; held in Cortona (Italy) from May 30 to June 3, 2016 .

Conics and Cubics is an accessible introduction to algebraic curves.

The material presented here can be divided into two parts.

A recent paper on subfactors of von Neumann factors has stimulated much research in von Neumann algebras.

This advanced textbook provides a comprehensive and unified account of the moment problem.

This monograph is concerned with the Shimura variety attached to a quaternion algebra over a totally real number field.

It is impossible to imagine modern mathematics without complex numbers.

The first modern, comprehensive introduction to central simple algebras for graduate students and researchers.

The theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way.

"e;An introduction to the ideas of algebraic geometry in the motivated context of system theory.

This volume presents selected papers resulting from the meeting at Sundance on enumerative algebraic geometry.

Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology.

This concise textbook gathers together key concepts and modern results on the theory of holomorphic foliations with singularities, offering a compelling vision on how the notion of foliation, usually linked to real functions and manifolds, can have an important role in the holomorphic world, as shown by modern results from mathematicians as H.

Previous publications on the generalization of the Thomae formulae to Zn curves have emphasized the theory's implications in mathematical physics and depended heavily on applied mathematical techniques.

This book offers a non-standard introduction to quantum mechanics and quantum field theory, approaching these topics from algebraic and geometric perspectives.

This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms.

This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises).

The aim of this book is to describe the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today.