Gröbner Basis, Mordell-Weil Lattices and Deformation of Singularities
Author : T. Shioda
Publisher :
Page : 18 pages
File Size : 18,50 MB
Release : 2009
Category : Elliptic surfaces
ISBN :
Author : T. Shioda
Publisher :
Page : 18 pages
File Size : 18,50 MB
Release : 2009
Category : Elliptic surfaces
ISBN :
Author : Matthias Schütt
Publisher : Springer Nature
Page : 431 pages
File Size : 48,76 MB
Release : 2019-10-17
Category : Mathematics
ISBN : 9813293012
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 : Jan Stevens
Publisher : Springer Science & Business Media
Page : 172 pages
File Size : 36,21 MB
Release : 2003
Category : Deformations of singularities
ISBN : 9783540005605
Author : Gert-Martin Greuel
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 22,28 MB
Release : 2007-02-23
Category : Mathematics
ISBN : 3540284192
Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.
Author :
Publisher :
Page : 868 pages
File Size : 48,36 MB
Release : 2007
Category : Mathematics
ISBN :
Author : Ákos Seress
Publisher : Cambridge University Press
Page : 292 pages
File Size : 14,15 MB
Release : 2003-03-17
Category : Mathematics
ISBN : 9780521661034
Table of contents
Author : Ronald A. DeVore
Publisher : Cambridge University Press
Page : 418 pages
File Size : 22,93 MB
Release : 2001-05-17
Category : Mathematics
ISBN : 9780521003490
Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.
Author : Sergei K. Lando
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 45,95 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 3540383611
Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.
Author : Kunihiko Kodaira
Publisher : Springer Nature
Page : 86 pages
File Size : 13,22 MB
Release : 2020-09-17
Category : Mathematics
ISBN : 9811573808
This is an English translation of the book in Japanese, published as the volume 20 in the series of Seminar Notes from The University of Tokyo that grew out of a course of lectures by Professor Kunihiko Kodaira in 1967. It serves as an almost self-contained introduction to the theory of complex algebraic surfaces, including concise proofs of Gorenstein's theorem for curves on a surface and Noether's formula for the arithmetic genus. It also discusses the behavior of the pluri-canonical maps of surfaces of general type as a practical application of the general theory. The book is aimed at graduate students and also at anyone interested in algebraic surfaces, and readers are expected to have only a basic knowledge of complex manifolds as a prerequisite.
Author : Arjen K. Lenstra
Publisher : Springer
Page : 138 pages
File Size : 15,97 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540478922
The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.