Algebraic geometry

Intersection cohomology assigns groups which satisfy a generalized form of Poincare duality over the rationals to a stratified singular space.

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Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration.

Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups.

Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks.

Hofstadter's Law: It always takes longer than you think it will take, even if you take into account Hofstadter's Law.

The book is devoted to the geometrical construction of the representations of Lusztig's small quantum groups at roots of unity.

The conjectural theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry.

Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties.

The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface.

The articles in this volume were written to commemorate Reinhold Remmert's 60th birthday in June, 1990.

The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent.

This is the first attempt of a systematic study of real Enriques surfaces culminating in their classification up to deformation.

These notes deal with deformation theory of complex analytic singularities and related objects.

The author develops a deformation theory for degenerations of complex curves; specifically, he treats deformations which induce splittings of the singular fiber of a degeneration.

Posn(R) and Eisenstein Series provides an introduction, requiring minimal prerequisites, to the analysis on symmetric spaces of positive definite real matrices as well as quotients of this space by the unimodular group of integral matrices.

Hofstadter's Law: It always takes longer than you think it will take, even if you take into account Hofstadter's Law.

Riemannian, symplectic and complex geometry are often studied by means ofsolutions to systems ofnonlinear differential equations, such as the equa- tions of geodesics, minimal surfaces, pseudoholomorphic curves and Yang- Mills connections.

by a more general quadratic algebra (possibly obtained by deformation) and then to derive Rq [G] by requiring it to possess the latter as a comodule.

Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R.

The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves.

This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002.

Complex geometry studies (compact) complex manifolds.

In the second edition we do not only correct errors, update references and improve some of the proofs of the text of the first edition, but also add a new chapter on singularities in arbitrary characteristic.

This text covers topics in algebraic geometry and commutative algebra with careful attention to their practical and computational aspects.

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.

Pluripotential theory is a very powerful tool in geometry, complex analysis and dynamics.

Vladimir Arnold was one of the great mathematical scientists of our time.

In the more than 100 years since the fundamental group was first introduced by Henri Poincare it has evolved to play an important role in different areas of mathematics.

The Abel Symposium 2009 "e;Combinatorial aspects of Commutative Algebra and Algebraic Geometry"e;, held at Voss, Norway, featured talks by leading researchers in the field.

This book brings together contributions by top-level experts from a wide range of topics in modern Hodge theory, originating in the authors' participation in the special years on Hodge theory at the Institute of Mathematical Sciences of the Americas (IMSA) in Miami.

This book brings together contributions by top-level experts from a wide range of topics in modern Hodge theory, originating in the authors' participation in the special years on Hodge theory at the Institute of Mathematical Sciences of the Americas (IMSA) in Miami.

This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto.

This volume contains the Proceedings of the conference "e;Complex and Differential Geometry 2009"e;, held at Leibniz Universitat Hannover, September 14 - 18, 2009.

It is a pleasure to welcome you to the proceedings of the second International Castle Meeting on Coding Theory and its Applications, held at La Mota Castle in Medina del Campo.

This volume contains revised papers that were presented at the international workshop entitled Computational Methods for Algebraic Spline Surfaces ("e;COMPASS"e;), which was held from September 29 to October 3, 2003, at Schlo Weinberg, Kefermarkt (A- tria).

The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives.

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This book contains a series of research papers on subjects related to the work of Niels Henrik Abel, written by some of the foremost specialists in their fields.

Algebraic Geometry provides an impressive theory targeting the understanding of geometric objects defined algebraically.

This monograph provides the first systematic treatment of the logarithmic Bogomolov-Tian-Todorov theorem.

This monograph provides the first systematic treatment of the logarithmic Bogomolov-Tian-Todorov theorem.

This book offers a comprehensive exploration of contemporary intersections between geometry, topology, and theoretical physics, emphasizing their mathematical foundations and applications.

This book offers a comprehensive exploration of contemporary intersections between geometry, topology, and theoretical physics, emphasizing their mathematical foundations and applications.

This book, consisting of two volumes, gives a contemporary account of the study of the class of projective algebraic surfaces known as Enriques surfaces.

This book, consisting of two volumes, gives a contemporary account of the study of the class of projective algebraic surfaces known as Enriques surfaces.

This book presents the notes originating from five series of lectures given at the CRM Barcelona in 21-25 June, 2021, during the "e;Higher homotopical structures"e; programme.