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Author: Arthur Ogus
Publisher: Cambridge University Press
Published: 2018-11-08
Total Pages: 559
ISBN-13: 1107187737
DOWNLOAD EBOOKA self-contained introduction to logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry.
Author: Renzo Cavalieri
Publisher: Springer Nature
Published: 2023-11-01
Total Pages: 163
ISBN-13: 3031394011
DOWNLOAD EBOOKThis 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.
Author: Shreeram Shankar Abhyankar
Publisher: World Scientific
Published: 2006
Total Pages: 758
ISBN-13: 9812568263
DOWNLOAD EBOOKThis 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.
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Published: 1992
Total Pages: 18
ISBN-13:
DOWNLOAD EBOOKAuthor: Siegfried Bosch
Publisher: Springer
Published: 2014-08-22
Total Pages: 255
ISBN-13: 3319044176
DOWNLOAD EBOOKThe 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: Robin Hartshorne
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 511
ISBN-13: 1475738498
DOWNLOAD EBOOKAn 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: C. Soulé
Publisher: Cambridge University Press
Published: 1994-09-15
Total Pages: 190
ISBN-13: 9780521477093
DOWNLOAD EBOOKAn account for graduate students of this new technique in diophantine geometry; includes account of higher dimensional theory.
Author: David Eisenbud
Publisher: Springer Science & Business Media
Published: 2006-04-06
Total Pages: 265
ISBN-13: 0387226397
DOWNLOAD EBOOKGrothendieck’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: Ilia Itenberg
Publisher: Springer Science & Business Media
Published: 2009-05-30
Total Pages: 113
ISBN-13: 3034600488
DOWNLOAD EBOOKThese notes present a polished introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The notes are based on a seminar at the Mathematical Research Center in Oberwolfach in October 2004. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.
Author: Spencer Bloch
Publisher: Cambridge University Press
Published: 2010-07-22
Total Pages: 155
ISBN-13: 1139487825
DOWNLOAD EBOOKSpencer Bloch's 1979 Duke lectures, a milestone in modern mathematics, have been out of print almost since their first publication in 1980, yet they have remained influential and are still the best place to learn the guiding philosophy of algebraic cycles and motives. This edition, now professionally typeset, has a new preface by the author giving his perspective on developments in the field over the past 30 years. The theory of algebraic cycles encompasses such central problems in mathematics as the Hodge conjecture and the Bloch–Kato conjecture on special values of zeta functions. The book begins with Mumford's example showing that the Chow group of zero-cycles on an algebraic variety can be infinite-dimensional, and explains how Hodge theory and algebraic K-theory give new insights into this and other phenomena.
