Complex Ball Quotients And Line Arrangements In The Projective Plane
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Complex Ball Quotients And Line Arrangements In The Projective Plane
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Author : Paula Tretkoff
language : en
Publisher: Princeton University Press
Release Date : 2016-02-16
Complex Ball Quotients And Line Arrangements In The Projective Plane written by Paula Tretkoff and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-16 with Mathematics categories.
This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. Paula Tretkoff emphasizes those finite covers that are free quotients of the complex two-dimensional ball. Tretkoff also includes background on the classical Gauss hypergeometric function of one variable, and a chapter on the Appell two-variable F1 hypergeometric function. The material in this book began as a set of lecture notes, taken by Tretkoff, of a course given by Friedrich Hirzebruch at ETH Zürich in 1996. The lecture notes were then considerably expanded by Hirzebruch and Tretkoff over a number of years. In this book, Tretkoff has expanded those notes even further, still stressing examples offered by finite covers of line arrangements. The book is largely self-contained and foundational material is introduced and explained as needed, but not treated in full detail. References to omitted material are provided for interested readers. Aimed at graduate students and researchers, this is an accessible account of a highly informative area of complex geometry.
Combinatorial Structures In Algebra And Geometry
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Author : Dumitru I. Stamate
language : en
Publisher: Springer Nature
Release Date : 2020-09-01
Combinatorial Structures In Algebra And Geometry written by Dumitru I. Stamate and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-01 with Mathematics categories.
This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constanța, Romania, on August 26-September 1, 2018. The works cover three fields of mathematics: algebra, geometry and discrete mathematics, discussing the latest developments in the theory of monomial ideals, algebras of graphs and local positivity of line bundles. Whereas interactions between algebra and geometry go back at least to Hilbert, the ties to combinatorics are much more recent and are subject of immense interest at the forefront of contemporary mathematics research. Transplanting methods between different branches of mathematics has proved very fruitful in the past – for example, the application of fixed point theorems in topology to solving nonlinear differential equations in analysis. Similarly, combinatorial structures, e.g., Newton-Okounkov bodies, have led to significant advances in our understanding of the asymptotic properties of line bundles in geometry and multiplier ideals in algebra. This book is intended for advanced graduate students, young scientists and established researchers with an interest in the overlaps between different fields of mathematics. A volume for the 24th edition of this conference was previously published with Springer under the title "Multigraded Algebra and Applications" (ISBN 978-3-319-90493-1).
Point Counting And The Zilber Pink Conjecture
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Author : Jonathan Pila
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
Point Counting And The Zilber Pink Conjecture written by Jonathan Pila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Mathematics categories.
Point-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink conjectures. The results combine ideas close to transcendence theory with the strong tameness properties of sets that are definable in an o-minimal structure, and thus the material treated connects ideas in model theory, transcendence theory, and arithmetic. This book describes the counting results and their applications along with their model-theoretic and transcendence connections. Core results are presented in detail to demonstrate the flexibility of the method, while wider developments are described in order to illustrate the breadth of the diophantine conjectures and to highlight key arithmetical ingredients. The underlying ideas are elementary and most of the book can be read with only a basic familiarity with number theory and complex algebraic geometry. It serves as an introduction for postgraduate students and researchers to the main ideas, results, problems, and themes of current research in this area.
Arrangements Of Hyperplanes
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Author : Peter Orlik
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Arrangements Of Hyperplanes written by Peter Orlik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space. Arrangements have emerged independently as important objects in various fields of mathematics such as combinatorics, braids, configuration spaces, representation theory, reflection groups, singularity theory, and in computer science and physics. This book is the first comprehensive study of the subject. It treats arrangements with methods from combinatorics, algebra, algebraic geometry, topology, and group actions. It emphasizes general techniques which illuminate the connections among the different aspects of the subject. Its main purpose is to lay the foundations of the theory. Consequently, it is essentially self-contained and proofs are provided. Nevertheless, there are several new results here. In particular, many theorems that were previously known only for central arrangements are proved here for the first time in completegenerality. The text provides the advanced graduate student entry into a vital and active area of research. The working mathematician will findthe book useful as a source of basic results of the theory, open problems, and a comprehensive bibliography of the subject.
Bulletin Of The American Mathematical Society
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Author :
language : en
Publisher:
Release Date : 1995
Bulletin Of The American Mathematical Society written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
Bulletin New Series Of The American Mathematical Society
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Author :
language : en
Publisher:
Release Date : 1995
Bulletin New Series Of The American Mathematical Society written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
Sitzungsberichte Der Berliner Mathematischen Gesellschaft
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Author : Berliner Mathematische Gesellschaft
language : de
Publisher:
Release Date : 2001
Sitzungsberichte Der Berliner Mathematischen Gesellschaft written by Berliner Mathematische Gesellschaft and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
List of members in 2.- Jahrg.
Locally Mixed Symmetric Spaces
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Author : Bruce Hunt
language : en
Publisher: Springer Nature
Release Date : 2021-09-04
Locally Mixed Symmetric Spaces written by Bruce Hunt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-04 with Mathematics categories.
What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations and gives each reader the "roter Faden", starting from the basics and proceeding towards quite advanced topics which lie at the intersection of differential and algebraic geometry, algebra and topology. Avoiding technicalities and assuming only a working knowledge of real Lie groups, the text provides a wealth of examples of symmetric spaces. The last two chapters deal with one particular case (Kuga fiber spaces) and a generalization (elliptic surfaces), both of which require some knowledge of algebraic geometry. Of interest to topologists, differential or algebraic geometers working in areas related to arithmetic groups, the book also offers an introduction to the ideas for non-experts.
Lecture Notes On Complex Analysis
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Author : Ivan Francis Wilde
language : en
Publisher: Imperial College Press
Release Date : 2006
Lecture Notes On Complex Analysis written by Ivan Francis Wilde and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Technology & Engineering categories.
This book is based on lectures presented over many years to second and third year mathematics students in the Mathematics Departments at Bedford College, London, and King's College, London, as part of the BSc. and MSci. program. Its aim is to provide a gentle yet rigorous first course on complex analysis.Metric space aspects of the complex plane are discussed in detail, making this text an excellent introduction to metric space theory. The complex exponential and trigonometric functions are defined from first principles and great care is taken to derive their familiar properties. In particular, the appearance of ã, in this context, is carefully explained.The central results of the subject, such as Cauchy's Theorem and its immediate corollaries, as well as the theory of singularities and the Residue Theorem are carefully treated while avoiding overly complicated generality. Throughout, the theory is illustrated by examples.A number of relevant results from real analysis are collected, complete with proofs, in an appendix.The approach in this book attempts to soften the impact for the student who may feel less than completely comfortable with the logical but often overly concise presentation of mathematical analysis elsewhere.
The Moduli Space Of Curves
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Author : R. Dijkgraaf
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-10-18
The Moduli Space Of Curves written by R. Dijkgraaf and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-18 with Mathematics categories.
The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory. Leading experts in the field explore in this volume both the structure of the moduli space of curves and its relationship with physics through quantum cohomology. Altogether, this is a lively volume that testifies to the ferment in the field and gives an excellent view of the state of the art for both mathematicians and theoretical physicists. It is a persuasive example of the famous Wignes comment, and its converse, on "the unreasonable effectiveness of mathematics in the natural science." Witteen’s conjecture in 1990 describing the intersection behavior of tautological classes in the cohomology of Mg arose directly from string theory. Shortly thereafter a stunning proof was provided by Kontsevich who, in this volume, describes his solution to the problem of counting rational curves on certain algebraic varieties and includes numerous suggestions for further development. The same problem is given an elegant treatment in a paper by Manin. There follows a number of contributions to the geometry, cohomology, and arithmetic of the moduli spaces of curves. In addition, several contributors address quantum cohomology and conformal field theory.