Analytic and algebraic geometry : common problems, different methods Jeffery McNeal, Mircea Mustata, editors

Format:

Book

Contributor:

McNeal, Jeffery D.

Mustata, Mircea, 1971-

Series:

IAS/Park City mathematics series v. 17

IAS/Park City Mathematics Series, 2472-5064 ; v. 17

Language:

English

Subjects (All):

Geometry, Analytic.

Geometry, Algebraic.

Physical Description:

1 online resource

Place of Publication:

Providence, R.I. American Mathematical Society [2010]

[Princeton, N.J.] Institute for Advanced Study [2010]

Summary:

"Analytic and algebraic geometers often study the same geometric structures but bring different methods to bear on them. While this dual approach has been spectacularly successful at solving problems, the language differences between algebra and analysis also represent a difficulty for students and researchers in geometry, particularly complex geometry. The PCMI program was designed to partially address this language gulf, by presenting some of the active developments in algebraic and analytic geometry in a form suitable for students on the 'other side' of the analysis-algebra language divide. One focal point of the summer school was multiplier ideals, a subject of wide current interest in both subjects. The present volume is based on a series of lectures at the PCMI summer school on analytic and algebraic geometry. The series is designed to give a high-level introduction to the advanced techniques behind some recent developments in algebraic and analytic geometry. The lectures contain many illustrative examples, detailed computations, and new perspectives on the topics presented, in order to enhance access of this material to non-specialists."--Publisher's description

Contents:

Introduction An introduction to things $\overline {\partial }$ Real and complex geometry meet the Cauchy-Riemann equations Three variations on a theme in complex analytic geometry Structure theorems for projective and Kähler varieties Lecture notes on rational polytopes and finite generation Introduction to resolution of singularities A short course on multiplier ideals Exercises in the birational geometry of algebraic varieties Higher dimensional minimal model program for varieties of log general type Lectures on flips and minimal models

Notes:

Includes bibliographical references

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Description based on print version record

Other Format:

Print version: Analytic and algebraic geometry :

ISBN:

9781470416317