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Abelian Coverings of the Complex Projective Plane Branched along Configurations of Real Lines

Author: Eriko Hironaka

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 98

ISBN-13: 082182564X

This work studies abelian branched coverings of smooth complex projective surfaces from the topological viewpoint. Geometric information about the coverings (such as the first Betti numbers of a smooth model or intersections of embedded curves) is related to topological and combinatorial information about the base space and branch locus. Special attention is given to examples in which the base space is the complex projective plane and the branch locus is a configuration of lines.

Abelian Coverings of the Complex Projective Plane Branched Along...

Author: Eriko Hironaka

Publisher: American Mathematical Society(RI)

Published: 2014-08-31

Total Pages: 98

ISBN-13: 9781470400798

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Arithmetic and Geometry Around Hypergeometric Functions

Author: Rolf-Peter Holzapfel

Publisher: Springer Science & Business Media

Published: 2007-06-28

Total Pages: 437

ISBN-13: 3764382848

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This volume comprises lecture notes, survey and research articles originating from the CIMPA Summer School Arithmetic and Geometry around Hypergeometric Functions held at Galatasaray University, Istanbul, June 13-25, 2005. It covers a wide range of topics related to hypergeometric functions, thus giving a broad perspective of the state of the art in the field.

Configuration Spaces

Author: Anders Björner

Publisher: Springer

Published: 2013-12-18

Total Pages: 547

ISBN-13: 8876424318

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These proceedings contain the contributions of some of the participants in the "intensive research period" held at the De Giorgi Research Center in Pisa, during the period May-June 2010. The central theme of this research period was the study of configuration spaces from various points of view. This topic originated from the intersection of several classical theories: Braid groups and related topics, configurations of vectors (of great importance in Lie theory and representation theory), arrangements of hyperplanes and of subspaces, combinatorics, singularity theory. Recently, however, configuration spaces have acquired independent interest and indeed the contributions in this volume go far beyond the above subjects, making it attractive to a large audience of mathematicians.

Hyperplane Arrangements

Author: Alexandru Dimca

Publisher: Springer

Published: 2017-03-28

Total Pages: 200

ISBN-13: 3319562215

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This textbook provides an accessible introduction to the rich and beautiful area of hyperplane arrangement theory, where discrete mathematics, in the form of combinatorics and arithmetic, meets continuous mathematics, in the form of the topology and Hodge theory of complex algebraic varieties. The topics discussed in this book range from elementary combinatorics and discrete geometry to more advanced material on mixed Hodge structures, logarithmic connections and Milnor fibrations. The author covers a lot of ground in a relatively short amount of space, with a focus on defining concepts carefully and giving proofs of theorems in detail where needed. Including a number of surprising results and tantalizing open problems, this timely book also serves to acquaint the reader with the rapidly expanding literature on the subject. Hyperplane Arrangements will be particularly useful to graduate students and researchers who are interested in algebraic geometry or algebraic topology. The book contains numerous exercises at the end of each chapter, making it suitable for courses as well as self-study.

Topology of Algebraic Varieties and Singularities

Author: José Ignacio Cogolludo-Agustín

Publisher: American Mathematical Soc.

Published: 2011

Total Pages: 496

ISBN-13: 0821848909

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This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honour of Anatoly Libgober's 60th birthday, held June 22-26, 2009, in Jaca, Spain.

On the Martingale Problem for Interactive Measure-Valued Branching Diffusions

Author: Edwin Arend Perkins

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 89

ISBN-13: 0821803581

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This book develops stochastic integration with respect to ``Brownian trees'' and its associated stochastic calculus, with the aim of proving pathwise existence and uniqueness in a stochastic equation driven by a historical Brownian motion. Perkins uses these results and a Girsanov-type theorem to prove that the martingale problem for the historical process associated with a wide class of interactive branching measure-valued diffusions (superprocesses) is well posed. The resulting measure-valued processes will arise as limits of the empirical measures of branching particle systems in which particles interact through their spatial motions or, to a lesser extent, through their branching rates.

Handbook of Geometry and Topology of Singularities II

Author: José Luis Cisneros-Molina

Publisher: Springer Nature

Published: 2021-11-01

Total Pages: 581

ISBN-13: 3030780244

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This is the second volume of the Handbook of the 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. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory and related topics. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Computational Algebraic and Analytic Geometry

Author: Mika Seppälä

Publisher: American Mathematical Soc.

Published: 2012

Total Pages: 242

ISBN-13: 0821868691

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This volume contains the proceedings of three AMS Special Sessions on Computational Algebraic and Analytic Geometry for Low-Dimensional Varieties held January 8, 2007, in New Orleans, LA; January 6, 2009, in Washington, DC; and January 6, 2011, in New Orleans, LA. Algebraic, analytic, and geometric methods are used to study algebraic curves and Riemann surfaces from a variety of points of view. The object of the study is the same. The methods are different. The fact that a multitude of methods, stemming from very different mathematical cultures, can be used to study the same objects makes this area both fascinating and challenging.

On the Classification of $C^*$-algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs

Author: Hongbing Su

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 83

ISBN-13: 0821826077

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This work shows that $K$-theoretic data is a complete invariant for certain inductive limit $C^*$-algebras. $C^*$-algebras of this kind are useful in studying group actions. Su gives a $K$-theoretic classification of the real rank zero $C^*$-algebras that can be expressed as inductive limits of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs or Hausdorff one-dimensional spaces defined as inverse limits of finite graphs. In addition, Su establishes a characterization for an inductive limit of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs to be real rank zero.