New Techniques in Resolution of Singularities / by Dan Abramovich, Anne Frühbis-Krüger, Michael Temkin, Jarosław Włodarczyk.

Format:

Book

Author/Creator:

Abramovich, D. (Dan)

Contributor:

ühbis-Krüger, Anne.

Temkin, Michael.

Włodarczyk, Jarosław.

Series:

Oberwolfach Seminars, 2296-5041 ; 50

Language:

English

Subjects (All):

Geometry, Algebraic.

Algebraic Geometry.

Local Subjects:

Algebraic Geometry.

Physical Description:

1 online resource (345 pages)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2023.

Summary:

Resolution of singularities is notorious as a difficult topic within algebraic geometry. Recent work, aiming at resolution of families and semistable reduction, infused the subject with logarithmic geometry and algebraic stacks, two techniques essential for the current theory of moduli spaces. As a byproduct a short, a simple and efficient functorial resolution procedure in characteristic 0 using just algebraic stacks was produced. The goals of the book, the result of an Oberwolfach Seminar, are to introduce readers to explicit techniques of resolution of singularities with access to computer implementations, introduce readers to the theories of algebraic stacks and logarithmic structures, and to resolution in families and semistable reduction methods.

Contents:

A Computational View on Hironaka’s Resolution of Singularities

Stacks for Everyone Who Cares About Varieties and Singularities

Introduction to Logarithmic Geometry

Birational Geometry Using Weighted Blowing Up

Relative and Logarithmic Resolution of Singularities

Weighted Resolution of Singularities. A Rees Algebra Approach

New Techniques in Resolution of Singularities: Open Problems.

Other Format:

Print version: Abramovich, Dan New Techniques in Resolution of Singularities

ISBN:

3-031-32115-4