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Author : Arthur Ogus
Publisher : Cambridge University Press
Page : 559 pages
File Size : 14,50 MB
Release : 2018-11-08
Category : Mathematics
ISBN : 1107187737
A self-contained introduction to logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry.
Author : Renzo Cavalieri
Publisher : Springer Nature
Page : 163 pages
File Size : 41,13 MB
Release : 2023-11-01
Category : Mathematics
ISBN : 3031394011
This book is based on the lectures given at the Oberwolfach Seminar held in Fall 2021. Logarithmic Gromov-Witten theory lies at the heart of modern approaches to mirror symmetry, but also opens up a number of new directions in enumerative geometry of a more classical flavour. Tropical geometry forms the calculus through which calculations in this subject are carried out. These notes cover the foundational aspects of this tropical calculus, geometric aspects of the degeneration formula for Gromov-Witten invariants, and the practical nuances of working with and enumerating tropical curves. Readers will get an assisted entry route to the subject, focusing on examples and explicit calculations.
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Publisher :
Page : 18 pages
File Size : 28,41 MB
Release : 1992
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Author : Shreeram Shankar Abhyankar
Publisher : World Scientific
Page : 758 pages
File Size : 40,83 MB
Release : 2006
Category : Mathematics
ISBN : 9812568263
This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel. Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author's lectures at Purdue University over the last few years.
Author : Bradd T. Hart
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 32,91 MB
Release : 2002
Category : Mathematics
ISBN : 0821827057
This thin volume contains three sets of lecture notes, representing recent developments in differential scales, o-minimality, and tame convergence theory. The first lecture outlines the basics of differential fields, and then addresses topics like differential varieties and tangent bundles, Kolchin's logarithmic derivative, and Manin's construction. The second describes added exponentation, T-convexity and tame extensions, piecewise linearity, the Wilkie inequality, and the valuation property. And the third considers the structure and varieties of finite algebra. No index. c. Book News Inc.
Author : A. Baker
Publisher : Cambridge University Press
Page : pages
File Size : 24,77 MB
Release : 2008-01-17
Category : Mathematics
ISBN : 1139468871
There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated celebrated discoveries of Faltings establishing the Mordell conjecture. This book gives an account of the theory of linear forms in the logarithms of algebraic numbers with special emphasis on the important developments of the past twenty-five years. The first part covers basic material in transcendental number theory but with a modern perspective. The remainder assumes some background in Lie algebras and group varieties, and covers, in some instances for the first time in book form, several advanced topics. The final chapter summarises other aspects of Diophantine geometry including hypergeometric theory and the André-Oort conjecture. A comprehensive bibliography rounds off this definitive survey of effective methods in Diophantine geometry.
Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 20,93 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 1475738498
An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Author : David Eisenbud
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 35,64 MB
Release : 2006-04-06
Category : Mathematics
ISBN : 0387226397
Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Author : Siegfried Bosch
Publisher : Springer
Page : 255 pages
File Size : 37,68 MB
Release : 2014-08-22
Category : Mathematics
ISBN : 3319044176
The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".
Author : C. Soulé
Publisher : Cambridge University Press
Page : 190 pages
File Size : 48,95 MB
Release : 1994-09-15
Category : Mathematics
ISBN : 9780521477093
An account for graduate students of this new technique in diophantine geometry; includes account of higher dimensional theory.