Algebraic

The goal of this book is to introduce the reader to some of the main techniques, ideas and concepts frequently used in modern geometry. It starts from scratch and it covers basic topics such as differential and integral calculus on manifolds, connections...

This volume is the proceedings of the online conference 'McKay correspondence, Mutation and Related Topics,' which was held at Kavli Institute for the Physics and Mathematics of the Universe (IPMU) in Japan in Summer in 2020.This volume consists of 15...

Algebraic geometry is more advanced with the completeness condition for projective or complete varieties. Many geometric properties are well described by the finiteness or the vanishing of sheaf cohomologies on such varieties. For non-complete varieties...

Spin/Pin-structures on vector bundles have long featured prominently in differential geometry, in particular providing part of the foundation for the original proof of the renowned Atiyah-Singer Index Theory. More recently, they have underpinned the...

Classical Deformation Theory is used for determining the completions of local rings of an eventual moduli space. When a moduli variety exists, the main result explored in the book is that the local ring in a closed point can be explicitly computed as an...

This book provides a gentle introduction to the foundations of Algebraic Geometry, starting from computational topics (ideals and homogeneous ideals, zero loci of ideals) up to increasingly intrinsic and abstract arguments, such as 'Algebraic Varieties',...

This book provides a gentle introduction to the foundations of Algebraic Geometry, starting from computational topics (ideals and homogeneous ideals, zero loci of ideals) up to increasingly intrinsic and abstract arguments, such as 'Algebraic Varieties',...

Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and...

Algebraic geometry in a traditional and fast developing research area in east Asia. There were many world leading algebraic geometers and there are remarkably increasing active mathematicians in the related area in the East Asia area including China,...

Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field. However, over a field of positive characteristics, many unpredictable phenomena arise where...

This book leads readers from a basic foundation to an advanced level understanding of geometry in advanced pure mathematics. Chapter by chapter, readers will be led from a foundation level understanding to advanced level understanding. This is the...

This is a proceedings of the 5th Franco-Japanese-Vietnamese Symposium on Singularities held in Kagoshima during 27th October - 3rd November, 2017. The main theme of the symposium was Singularity Theory in a broad sense, including complex and real...

Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations...

This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces. The main challenges are to understand the global and local structure of arc...

These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties. These quotient varieties...

This is a book about Mathematics but not a book of Mathematics. It is an attempt, between the serious and facetious, of conveying the idea that a mathematical thought is the result of different experiences, geographical and social factors. Even though it...

'The presentation is modeled on the discursive style of the Bourbaki collective, and the coverage of topics is rich and varied. Grandis has provided a large selection of exercises and has sprinkled orienting comments throughout. For an undergraduate...

This monograph studies decompositions of the Jacobian of a smooth projective curve, induced by the action of a finite group, into a product of abelian subvarieties. The authors give a general theorem on how to decompose the Jacobian which works in many...

In his 1974 seminal paper 'Elliptic modules', V G Drinfeld introduced objects into the arithmetic geometry of global function fields which are nowadays known as 'Drinfeld Modules'. They have many beautiful analogies with elliptic curves and abelian...

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum...

Measures and integralsBook InformationISBN 9780691095790Author John Von NeumannFormat PaperbackPage Count 116Imprint Princeton University PressPublisher Princeton University PressWeight(grams) 255g

The description for this book, Singular Points of Complex Hypersurfaces. (AM-61), will be forthcoming.About the AuthorJohn Milnor is professor of mathematics and codirector of the Institute for Mathematical Sciences at Stony Brook University, State...

For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf...

Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and...

A foundational account of a new construction in the p-adic Langlands correspondence Motivated by the p-adic Langlands program, this book constructs stacks that algebraize Mazur's formal deformation rings of local Galois representations. More precisely,...

Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, Janos Kollar provides a comprehensive treatment of the characteristic 0 case. He describes more than a dozen proofs for curves, many based on the...

This volume, first published in 2000, presents a classical approach to the foundations and development of the geometry of vector fields, describing vector fields in three-dimensional Euclidean space, triply-orthogonal systems and applications in...

The D(2) problem is a fundamental problem in low dimensional topology. In broad terms, it asks when a three-dimensional space can be continuously deformed into a two-dimensional space without changing the essential algebraic properties of the spaces...

This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by...

This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory...

In algebraic geometry and theoretical physics, mirror symmetry refers to the relationship between two Calabi–Yau manifolds which appear very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory...

The original goal that ultimately led to this volume was the construction of "motivic cohomology theory," whose existence was conjectured by A. Beilinson and S. Lichtenbaum. This is achieved in the book's fourth paper, using results of the...

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...

The first book on the explicit birational geometry of complex algebraic threefolds arising from the minimal model program, this text is sure to become an essential reference in the field of birational geometry. Threefolds remain the interface between low...

Don't be a square! Strengthen your geometrical skills Lots of students need extra practice to master geometry. Thankfully, there's Geometry Workbook For Dummies. Packed with hundreds of practice problems and easy-to-understand concept explanations, this...

This book provides a systematic, comprehensive and up-to-date account of the recent developments in non-commutative geometry, at a pedagogical level. It does not go into the details of rigorous (advanced level) mathematical formulation of non-commutative...

This book provides an introduction to categorical Donaldson-Thomas (DT) theory, a rapidly developing field which has close links to enumerative geometry, birational geometry, geometric representation theory and classical moduli problems in algebraic...

This monograph presents new research on Arakelov geometry over adelic curves, a novel theory of arithmetic geometry developed by the authors. It explores positivity conditions and establishes the Hilbert-Samuel formula and the equidistribution theorem in...

This textbook is intended to be accessible to any second-year undergraduate in mathematics who has attended courses on basic real analysis and linear algebra. It is meant to help students to appreciate the diverse specialized mathematics courses offered...

Dieses Buch richtet sich an Studierende der Mathematik, die die Anfängervorlesungen in Analysis und Linearer Algebra gemeistert haben. Es ist gedacht als Orientierungshilfe für die Vielzahl an spezialisierten Fachveranstaltungen in den mittleren und...