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

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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.

Configuration Spaces
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.

Topological Invariants of the Complement to Arrangements of Rational Plane Curves
Topological Invariants of the Complement to Arrangements of Rational Plane Curves

Author: José Ignacio Cogolludo-Agustín

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 97

ISBN-13: 0821829424

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The authors analyse two topological invariants of an embedding of an arrangement of rational plane curves in the projective complex plane, namely, the cohomology ring of the complement and the characteristic varieties. Their main result states that the cohomology ring of the complement to a rational arrangement is generated by logarithmic 1 and 2-forms and its structure depends on a finite number of invariants of the curve (its combinatorial type).

Topology of Algebraic Varieties and Singularities
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
On the Martingale Problem for Interactive Measure-Valued Branching Diffusions

Author: Edwin Arend Perkins

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 102

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
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
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
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: 98

ISBN-13: 0821826077

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In this paper a [italic capital]K-theoretic classification is given of the real rank zero [italic capital]C*-algebras that can be expressed as inductive limits of sequences of finite direct sums of matrix algebras over finite connected graphs (possibly with multiple vertices). The special case that the graphs are circles is due to Elliott.

$(16,6)$ Configurations and Geometry of Kummer Surfaces in ${\mathbb P}^3$
$(16,6)$ Configurations and Geometry of Kummer Surfaces in ${\mathbb P}^3$

Author: Maria del Rosario Gonzalez-Dorrego

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 114

ISBN-13: 0821825747

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The philosophy of the first part of this work is to understand (and classify) Kummer surfaces by studying (16, 6) configurations. Chapter 1 is devoted to classifying (16, 6) configurations and studying their manifold symmetries and the underlying questions about finite subgroups of [italic capitals]PGL4([italic]k). In chapter 2 we use this information to give a complete classification of Kummer surfaces together with explicit equations and the explicit description of their singularities.