Lattices and Their Applications to Rational Elliptic Surfaces PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Lattices and Their Applications to Rational Elliptic Surfaces PDF full book. Access full book title Lattices and Their Applications to Rational Elliptic Surfaces by Gretchen Rimmasch. Download full books in PDF and EPUB format.
Author: Gretchen Rimmasch
Publisher:
ISBN:
Category : Lattice theory
Languages : en
Pages : 70
Get Book Here
Book Description
This thesis discusses some of the invariants of rational elliptic surfaces, namely the Mordell-Weil Group, Mordell-Weil Lattice, and another lattice which will be called the Shioda Lattice. It will begin with a brief overview of rational elliptic surfaces, followed by a discussion of lattices, root systems and Dynkin diagrams. Known results of several authors will then be applied to determine the groups and lattices associated with a given rational elliptic surface, along with a discussion of the uses of these groups and lattices in classifying surfaces.
Author: Matthias Schütt
Publisher: Springer Nature
ISBN: 9813293012
Category : Mathematics
Languages : en
Pages : 431
Get Book Here
Book Description
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.
Author: Gretchen Rimmasch
Publisher:
ISBN:
Category : Lattice theory
Languages : en
Pages : 70
Get Book Here
Book Description
This thesis discusses some of the invariants of rational elliptic surfaces, namely the Mordell-Weil Group, Mordell-Weil Lattice, and another lattice which will be called the Shioda Lattice. It will begin with a brief overview of rational elliptic surfaces, followed by a discussion of lattices, root systems and Dynkin diagrams. Known results of several authors will then be applied to determine the groups and lattices associated with a given rational elliptic surface, along with a discussion of the uses of these groups and lattices in classifying surfaces.
Author: Rick Miranda
Publisher:
ISBN:
Category : Curves, Elliptic
Languages : en
Pages : 126
Get Book Here
Book Description
Author: Henry Paul Miranda
Publisher:
ISBN:
Category : Geometry, Algebraic
Languages : en
Pages : 196
Get Book Here
Book Description
Author: Julie B. Rogers
Publisher:
ISBN:
Category : Curves, Elliptic
Languages : en
Pages : 103
Get Book Here
Book Description
Author: Henry P. Miranda
Publisher:
ISBN:
Category :
Languages : en
Pages : 74
Get Book Here
Book Description
Author: Alexei N. Skorobogatov
Publisher: Cambridge University Press
ISBN: 1107245265
Category : Mathematics
Languages : en
Pages : 470
Get Book Here
Book Description
Torsors, also known as principal bundles or principal homogeneous spaces, are ubiquitous in mathematics. The purpose of this book is to present expository lecture notes and cutting-edge research papers on the theory and applications of torsors and étale homotopy, all written from different perspectives by leading experts. Part one of the book contains lecture notes on recent uses of torsors in geometric invariant theory and representation theory, plus an introduction to the étale homotopy theory of Artin and Mazur. Part two of the book features a milestone paper on the étale homotopy approach to the arithmetic of rational points. Furthermore, the reader will find a collection of research articles on algebraic groups and homogeneous spaces, rational and K3 surfaces, geometric invariant theory, rational points, descent and the Brauer–Manin obstruction. Together, these give a state-of-the-art view of a broad area at the crossroads of number theory and algebraic geometry.
Author: Laurentiu Paunescu
Publisher: World Scientific
ISBN: 9812706895
Category : Mathematics
Languages : en
Pages : 475
Get Book Here
Book Description
The modern theory of singularities provides a unifying theme that runs through fields of mathematics as diverse as homological algebra and Hamiltonian systems. It is also an important point of reference in the development of a large part of contemporary algebra, geometry and analysis. Presented by internationally recognized experts, the collection of articles in this volume yields a significant cross-section of these developments. The wide range of surveys includes an authoritative treatment of the deformation theory of isolated complex singularities by prize-winning researcher K Miyajima. Graduate students and even ambitious undergraduates in mathematics will find many research ideas in this volume and non-experts in mathematics can have an overview of some classic and fundamental results in singularity theory. The explanations are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.
Author: John McKay
Publisher: American Mathematical Soc.
ISBN: 0821828797
Category : Mathematics
Languages : en
Pages : 280
Get Book Here
Book Description
This volume contains the proceedings of the Moonshine workshop held at the Centre de Recherches Mathematiques (CRM) in Montreal. In this volume, all the classical Moonshine themes are presented, namely the Monster simple group and other finite groups, automorphic functions and forms and related congruence groups, and vertex algebras and their representations. These topics appear in either a pure form or in a blend of algebraic geometry dealing with algebraic surfaces, Picard-Fuchsequations, and hypergeometric functions.
Author: J. Hietarinta
Publisher: Cambridge University Press
ISBN: 1107042720
Category : Mathematics
Languages : en
Pages : 461
Get Book Here
Book Description
A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.
