ENGLISH

Donaldson Type Invariants for Algebraic Surfaces: Transition of Moduli Stacks

By Takuro Mochizuki (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2009
ISBN
3540939121, 9783540939122
DOI
10.1007/978-3-540-93913-9
LCC
QA571 .M588 2009
Open Library ID
OL25007564M
Language
english
Format
PDF
Filesize
3 MB (2842323 bytes)
Series
Lecture Notes in Mathematics 1972
Edition
1
Pages
383\404
Scanned
no
Time added
2011-06-04 13:46:07
Algebraic Geometry

Description

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!

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