Families of Varieties of General Type
Title | Families of Varieties of General Type PDF eBook |
Author | János Kollár |
Publisher | Cambridge University Press |
Pages | 492 |
Release | 2023-04-20 |
Genre | Mathematics |
ISBN | 1009346148 |
This book establishes the moduli theory of stable varieties, giving the optimal approach to understanding families of varieties of general type. Starting from the Deligne–Mumford theory of the moduli of curves and using Mori's program as a main tool, the book develops the techniques necessary for a theory in all dimensions. The main results give all the expected general properties, including a projective coarse moduli space. A wealth of previously unpublished material is also featured, including Chapter 5 on numerical flatness criteria, Chapter 7 on K-flatness, and Chapter 9 on hulls and husks.
Families of Varieties of General Type
Title | Families of Varieties of General Type PDF eBook |
Author | János Kollár |
Publisher | Cambridge University Press |
Pages | 491 |
Release | 2023-04-30 |
Genre | Mathematics |
ISBN | 1009346105 |
The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.
Classification of Higher Dimensional Algebraic Varieties
Title | Classification of Higher Dimensional Algebraic Varieties PDF eBook |
Author | Christopher D. Hacon |
Publisher | Springer Science & Business Media |
Pages | 206 |
Release | 2011-02-02 |
Genre | Mathematics |
ISBN | 3034602901 |
Higher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model program are discussed, and an introduction to the theory of moduli spaces is presented.
Number Theory
Title | Number Theory PDF eBook |
Author | Canadian Number Theory Association. Conference |
Publisher | American Mathematical Soc. |
Pages | 426 |
Release | 1999 |
Genre | Mathematics |
ISBN | 0821809644 |
This book contains papers presented at the Fifth Canadian Number Theory Association (CNTA) conference held at Carleton University Ottawa, Ontario. The invited speakers focused on arithmetic algebraic geometry and elliptic curves, diophantine problems, analytic number theory, and algebraic and computational number theory. The contributed talks represented a wide variety of areas in number theory. David Boyd gave an hour-long talk on Mahler's Measure and Elliptic Curves. This lecture was open to the public and attracted a large audience from outside the conference.
Theory of Algebraic Surfaces
Title | Theory of Algebraic Surfaces PDF eBook |
Author | Kunihiko Kodaira |
Publisher | Springer Nature |
Pages | 86 |
Release | 2020-09-17 |
Genre | 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.
Higher Dimensional Varieties and Rational Points
Title | Higher Dimensional Varieties and Rational Points PDF eBook |
Author | Károly Jr. Böröczky |
Publisher | Springer Science & Business Media |
Pages | 307 |
Release | 2013-12-11 |
Genre | Mathematics |
ISBN | 3662051230 |
Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on "Higher Dimensional Varieties and Rational Points" held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area.
Recent Progress in Arithmetic and Algebraic Geometry
Title | Recent Progress in Arithmetic and Algebraic Geometry PDF eBook |
Author | Yasuyuki Kachi |
Publisher | American Mathematical Soc. |
Pages | 186 |
Release | 2005 |
Genre | Mathematics |
ISBN | 0821834010 |
This proceedings volume resulted from the John H. Barrett Memorial Lecture Series held at the University of Tennessee (Knoxville). The articles reflect recent developments in algebraic geometry. It is suitable for graduate students and researchers interested in algebra and algebraic geometry.