Donaldson Type Invariants for Algebraic Surfaces : Transition of Moduli Stacks / by Takuro Mochizuki.

Format:

Book

Author/Creator:

Mochizuki, Takuro, 1972- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1972.

Lecture Notes in Mathematics, 0075-8434 ; 1972

Language:

English

Subjects (All):

Geometry, Algebraic.

Algebraic Geometry.

Local Subjects:

Algebraic Geometry.

Physical Description:

1 online resource (XXIII, 383 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.

System Details:

text file PDF

Summary:

We are defining and studying an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface.We are interested in relations among the invariants, which are natural generalizations of the "wall-crossing formula" and the "Witten conjecture" for classical Donaldson invariants. Our goal is to obtain a weaker version of these relations, by systematically using the intrinsic smoothness of moduli spaces. According to the recent excellent work of L. Goettsche, H. Nakajima and K. Yoshioka, the wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case!

Contents:

Preliminaries

Parabolic L-Bradlow Pairs

Geometric Invariant Theory and Enhanced Master Space

Obstruction Theories of Moduli Stacks and Master Spaces

Virtual Fundamental Classes

Invariants.

Other Format:

Printed edition:

ISBN:

9783540939139

Access Restriction:

Restricted for use by site license.