16 6 Configurations And Geometry Of Kummer Surfaces In Mathbb P 3
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16 6 Configurations And Geometry Of Kummer Surfaces In
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Author : Maria del Rosario Gonzalez-Dorrego
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-08-31
16 6 Configurations And Geometry Of Kummer Surfaces In written by Maria del Rosario Gonzalez-Dorrego and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-31 with MATHEMATICS categories.
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.
16 6 Configurations And Geometry Of Kummer Surfaces In Mathbb P 3
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Author : Maria del Rosario Gonzalez-Dorrego
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
16 6 Configurations And Geometry Of Kummer Surfaces In Mathbb P 3 written by Maria del Rosario Gonzalez-Dorrego and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
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.
16 6 Configurations And Geometry Of Kummer Surfaces In
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Author : Maria Gonzalez-Dorrego
language : it
Publisher:
Release Date : 1994
16 6 Configurations And Geometry Of Kummer Surfaces In written by Maria Gonzalez-Dorrego and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Some Special Properties Of The Adjunction Theory For 3 Folds In Mathbb P 5
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Author : Mauro Beltrametti
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Some Special Properties Of The Adjunction Theory For 3 Folds In Mathbb P 5 written by Mauro Beltrametti and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This work studies the adjunction theory of smooth 3-folds in P]5. Because of the many special restrictions on such 3-folds, the structure of the adjunction theoretic reductions are especially simple, e.g. the 3-fold equals its first reduction, the second reduction is smooth except possibly for a few explicit low degrees, and the formulae relating the projective invariants of the given 3-fold with the invariants of its second reduction are very explicit. Tables summarizing the classification of such 3-folds up to degree 12 are included. Many of the general results are shown to hold for smooth projective n-folds embedded in P]N with N 2n -1.
Mordell Weil Lattices
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Author : Matthias Schütt
language : en
Publisher: Springer Nature
Release Date : 2019-10-17
Mordell Weil Lattices written by Matthias Schütt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-17 with Mathematics categories.
This book lays out the theory of Mordell–Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics. The book presents all the ingredients entering into the theory of Mordell–Weil lattices in detail, notably, relevant portions of lattice theory, elliptic curves, and algebraic surfaces. After defining Mordell–Weil lattices, the authors provide several applications in depth. They start with the classification of rational elliptic surfaces. Then a useful connection with Galois representations is discussed. By developing the notion of excellent families, the authors are able to design many Galois representations with given Galois groups such as the Weyl groups of E6, E7 and E8. They also explain a connection to the classical topic of the 27 lines on a cubic surface. Two chapters deal with elliptic K3 surfaces, a pulsating area of recent research activity which highlights many central properties of Mordell–Weil lattices. Finally, the book turns to the rank problem—one of the key motivations for the introduction of Mordell–Weil lattices. The authors present the state of the art of the rank problem for elliptic curves both over Q and over C(t) and work out applications to the sphere packing problem. Throughout, the book includes many instructive examples illustrating the theory.
Kummer S Quartic Surface
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Author : Ronald William Henry Turnbull Hudson
language : en
Publisher: Cambridge University Press
Release Date : 1990-10-11
Kummer S Quartic Surface written by Ronald William Henry Turnbull Hudson 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 1990-10-11 with Mathematics categories.
Many questions involving the theory of surfaces, such as the classification of quartic surfaces, the description of moduli spaces for abelian surfaces, and the automorphism group of a Kummer surface, are touched upon in this volume.
The Arithmetic Of Elliptic Curves
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Author : Joseph H. Silverman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Arithmetic Of Elliptic Curves written by Joseph H. Silverman 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.
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.
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.
Six Lectures On Commutative Algebra
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Author : J. Elias
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-17
Six Lectures On Commutative Algebra written by J. Elias 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 2010-03-17 with Mathematics categories.
Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful overview of the field and recent developments in it. Reviews "All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples." - Acta Scientiarum Mathematicarum Avramov lecture: "... it contains all the major results [on infinite free resolutions], it explains carefully all the different techniques that apply, it provides complete proofs (...). This will be extremely helpful for the novice as well as the experienced." - Mathematical reviews Huneke lecture: "The topic is tight closure, a theory developed by M. Hochster and the author which has in a short time proved to be a useful and powerful tool. (...) The paper is extremely well organized, written, and motivated." - Zentralblatt MATH Schenzel lecture: "... this paper is an excellent introduction to applications of local cohomology." - Zentralblatt MATH Valla lecture: "... since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory." - Mathematical reviews Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relations between them, and how to compute them." - Zentralblatt MATH
Advances In Geometry And Lie Algebras From Supergravity
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Author : Pietro Giuseppe Frè
language : en
Publisher: Springer
Release Date : 2018-02-24
Advances In Geometry And Lie Algebras From Supergravity written by Pietro Giuseppe Frè and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-24 with Science categories.
This book aims to provide an overview of several topics in advanced differential geometry and Lie group theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry/supergravity. The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject.