Algebraic geometry

Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics.

Volterra Stieltjes-Integral Equations

Differential Equations and Applications

This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field.

Eine verständliche, konzise und immer flüssige Einführung in die Algebra, die insbesondere durch ihre sorgfältige didaktische Aufbereitung bei vielen Studenten Freunde finden wird.

Divisor Theory in Module Categories

This text started out as a revised version of Buildings by the second-named author [53], but it has grown into a much more voluminous book.

Assuming that the reader is familiar with sheaf theory, the book gives a self-contained introduction to the theory of constructible sheaves related to many kinds of singular spaces, such as cell complexes, triangulated spaces, semialgebraic and subanalytic sets, complex algebraic or analytic sets, stratified spaces, and quotient spaces.

Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses.

Locally Compact Semi-Algebras

In the fall of 1992 I was invited by Professor Changho Keem to visit Seoul National University and give a series of talks.

The exposition studies projective models of K3 surfaces whose hyperplane sections are non-Clifford general curves.

This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology.

This book collects the scientific contributions of a group of leading experts who took part in the INdAM Meeting held in Cortona in September 2014.

Eine verständliche, konzise und immer flüssige Einführung in die Algebra, die insbesondere durch ihre sorgfältige didaktische Aufbereitung bei vielen Studenten Freunde finden wird.

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics.

Grids are special families of tripotents in Jordan triple systems.

Positivity is one of the most basic mathematical concepts.

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

Hopf Spaces

This is the second volume of the new subseries "e;Invariant Theory and Algebraic Transformation Groups"e;.

A comprehensive, self-contained treatment presenting general results of the theory.

This book discusses the changing conceptions about the relationship between geometry and arithmetic within the Euclidean tradition that developed in the British context of the sixteenth and seventeenth century.

This is the sixth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research.

An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.

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

This is an English translation of the book in Japanese, published as the volume 20 in the series of Seminar Notes from The University of Tokyo that grew out of a course of lectures by Professor Kunihiko Kodaira in 1967.

Due to the lack of proper bibliographical sources stratification theory seems to be a "e;mysterious"e; subject in contemporary mathematics.

This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces.

Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves.

The second edition presents schemes, simplicial sets, higher categories, model categories, derived algebraic geometry, and spectral algebraic geometry in a self-contained manner.

Now in new trade paper editions, these classic biographies of two of the greatest 20th Century mathematicians are being released under the Copernicus imprint.

These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries.

In the 19 years which passed since the first edition was published, several important developments have taken place in the theory of surfaces.

In this book we consider deep and classical results of homotopy theory like the homological Whitehead theorem, the Hurewicz theorem, the finiteness obstruction theorem of Wall, the theorems on Whitehead torsion and simple homotopy equivalences, and we characterize axiomatically the assumptions under which such results hold.

This lecture notes volume presents significant contributions from the "e;Algebraic Geometry and Number Theory"e; Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014.

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

Affine algebraic geometry has progressed remarkably in the last half a century, and its central topics are affine spaces and affine space fibrations.

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject.

This book includes selected papers presented at the MIMS (Mediterranean Institute for the Mathematical Sciences) - GGTM (Geometry and Topology Grouping for the Maghreb) conference, held in memory of Mohammed Salah Baouendi, a most renowned figure in the field of several complex variables, who passed away in 2011.

An incredible season for algebraic geometry flourished in Italy between 1860, when Luigi Cremona was assigned the chair of Geometria Superiore in Bologna, and 1959, when Francesco Severi published the last volume of the treatise on algebraic systems over a surface and an algebraic variety.

This book makes a systematic study of the relations between the etale cohomology of a scheme and the orderings of its residue fields.

This book is about modern algebraic geometry.

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry.

The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group.