166 Configurations And Geometry Of Kummer Surfaces In Mathbb P3

Author : Maria del Rosario Gonzalez-Dorrego
Publisher : American Mathematical Society(RI)
ISBN 13 : 9781470400897
Total Pages : 114 pages
Book Rating : 4.98/5 ( download)

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Download or read book 16,6 Configurations and Geometry of Kummer Surfaces in written by Maria del Rosario Gonzalez-Dorrego and published by American Mathematical Society(RI). This book was released on 2014-08-31 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph studies the geometry of a Summer surface in P ]3 and of its minimal desingularization, which is a K3 surface (here k is an algebraically closed field of characteristic different from 2). This Kummer surface is a quartic surface with sixteen nodes as its only singularities. These nodes give rise to a configuration of sixteen points and sixteen planes in P ]3 such that each plane contains exactly six points and each point belongs to exactly six planes (this is called a (16, 6) configuration). A Kummer surface is uniquely determined by its set of nodes. Gonzalez_Dorrego classifies (16, 6) configurations and studies their manifold symmetries and the underlying questions about finite subgroups of PGL [4 ( k ). She uses this information to give a complete classification of Kummer surfaces with explicit equations and explicit descriptions of their singularities. In addition, the beautiful connections to the theory of K3 surfaces and abelian varieties are studied.

Author : Maria del Rosario Gonzalez-Dorrego
Publisher : American Mathematical Soc.
ISBN 13 : 0821825747
Total Pages : 101 pages
Book Rating : 4.47/5 ( download)

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Download or read book $(16,6)$ Configurations and Geometry of Kummer Surfaces in ${\mathbb P}^3$ written by Maria del Rosario Gonzalez-Dorrego and published by American Mathematical Soc.. This book was released on 1994 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Valery A. Gritsenko
Publisher : Springer Nature
ISBN 13 : 3030424006
Total Pages : 422 pages
Book Rating : 4.08/5 ( download)

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Download or read book Partition Functions and Automorphic Forms written by Valery A. Gritsenko and published by Springer Nature. This book was released on 2020-07-09 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.

Author : Diane Maclagan
Publisher : American Mathematical Society
ISBN 13 : 1470468565
Total Pages : 363 pages
Book Rating : 4.69/5 ( download)

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Download or read book Introduction to Tropical Geometry written by Diane Maclagan and published by American Mathematical Society. This book was released on 2021-12-13 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature. This wonderful book will appeal to students and researchers of all stripes: it begins at an undergraduate level and ends with deep connections to toric varieties, compactifications, and degenerations. In between, the authors provide the first complete proofs in book form of many fundamental results in the subject. The pages are sprinkled with illuminating examples, applications, and exercises, and the writing is lucid and meticulous throughout. It is that rare kind of book which will be used equally as an introductory text by students and as a reference for experts. —Matt Baker, Georgia Institute of Technology Tropical geometry is an exciting new field, which requires tools from various parts of mathematics and has connections with many areas. A short definition is given by Maclagan and Sturmfels: “Tropical geometry is a marriage between algebraic and polyhedral geometry”. This wonderful book is a pleasant and rewarding journey through different landscapes, inviting the readers from a day at a beach to the hills of modern algebraic geometry. The authors present building blocks, examples and exercises as well as recent results in tropical geometry, with ingredients from algebra, combinatorics, symbolic computation, polyhedral geometry and algebraic geometry. The volume will appeal both to beginning graduate students willing to enter the field and to researchers, including experts. —Alicia Dickenstein, University of Buenos Aires, Argentina

Author : Z.S. Agranovich
Publisher : Courier Dover Publications
ISBN 13 : 0486842495
Total Pages : 307 pages
Book Rating : 4.93/5 ( download)

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Download or read book The Inverse Problem of Scattering Theory written by Z.S. Agranovich and published by Courier Dover Publications. This book was released on 2020-05-21 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph by two Soviet experts in mathematical physics was a major contribution to inverse scattering theory. The two-part treatment examines the boundary-value problem with and without singularities. 1963 edition.

Author : Ilias S. Kotsireas
Publisher : Springer
ISBN 13 : 331932859X
Total Pages : 628 pages
Book Rating : 4.91/5 ( download)

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Download or read book Mathematical Aspects of Computer and Information Sciences written by Ilias S. Kotsireas and published by Springer. This book was released on 2016-04-16 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015, held in Berlin, Germany, in November 2015. The 48 revised papers presented together with 7 invited papers were carefully reviewed and selected from numerous submissions. The papers are grouped in topical sections on curves and surfaces, applied algebraic geometry, cryptography, verified numerical computation, polynomial system solving, managing massive data, computational theory of differential and difference equations, data and knowledge exploration, algorithm engineering in geometric computing, real complexity: theory and practice, global optimization, and general session.

Author : Jean-Marc Luck
Publisher : Springer Science & Business Media
ISBN 13 : 3642754058
Total Pages : 324 pages
Book Rating : 4.50/5 ( download)

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Download or read book Number Theory and Physics written by Jean-Marc Luck and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 7 Les Houches Number theory, or arithmetic, sometimes referred to as the queen of mathematics, is often considered as the purest branch of mathematics. It also has the false repu tation of being without any application to other areas of knowledge. Nevertheless, throughout their history, physical and natural sciences have experienced numerous unexpected relationships to number theory. The book entitled Number Theory in Science and Communication, by M.R. Schroeder (Springer Series in Information Sciences, Vol. 7, 1984) provides plenty of examples of cross-fertilization between number theory and a large variety of scientific topics. The most recent developments of theoretical physics have involved more and more questions related to number theory, and in an increasingly direct way. This new trend is especially visible in two broad families of physical problems. The first class, dynamical systems and quasiperiodicity, includes classical and quantum chaos, the stability of orbits in dynamical systems, K.A.M. theory, and problems with "small denominators", as well as the study of incommensurate structures, aperiodic tilings, and quasicrystals. The second class, which includes the string theory of fundamental interactions, completely integrable models, and conformally invariant two-dimensional field theories, seems to involve modular forms and p adic numbers in a remarkable way.

Author : David Mumford
Publisher :
ISBN 13 : 9789380250809
Total Pages : 0 pages
Book Rating : 4.00/5 ( download)

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Download or read book Algebraic Geometry II written by David Mumford and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several generations of students of algebraic geometry have learned the subject from David Mumford's fabled "Red Book" containing notes of his lectures at Harvard University. This book contains what Mumford had intended to be Volume II. It covers the material in the "Red Book" in more depth with several more topics added.

Author : John Willard Milnor
Publisher : American Mathematical Soc.
ISBN 13 : 0821848755
Total Pages : 323 pages
Book Rating : 4.53/5 ( download)

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Download or read book Collected Papers of John Milnor written by John Willard Milnor and published by American Mathematical Soc.. This book was released on 2009 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers of one of the best modern geometers and topologists, John Milnor, on various topics related to the notion of the fundamental group. The volume contains sixteen papers divided into four parts: Knot theory, Free actions on spheres, Torsion, and Three-dimensional manifolds. Each part is preceded by an introduction containing the author's comments on further development of the subject. Although some of the papers were written quite a while ago, they appear more modern than many of today's publications. Milnor's excellent, clear, and laconic style makes the book a real treat. This volume is highly recommended to a broad mathematical audience, and, in particular, to young mathematicians who will certainly benefit from their acquaintance with Milnor's mode of thinking and writing.

Author : Christian Janot
Publisher : World Scientific Publishing Company
ISBN 13 :
Total Pages : 456 pages
Book Rating : 4.16/5 ( download)

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Download or read book Quasicrystalline Materials written by Christian Janot and published by World Scientific Publishing Company. This book was released on 1988 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: