Donaldson Type Invariants for Algebraic Surfaces: Transition of Moduli Stacks
Takuro Mochizuki
Bok Engelsk 2009
| Annen tittel | |
|---|---|
| Utgitt | Berlin : Springer , c2009
|
| Omfang | 1 online resource (XXIII, 383 p.)
|
| Opplysninger | Bibliographic Level Mode of Issuance: Monograph. - Preliminaries -- Parabolic L-Bradlow Pairs -- Geometric Invariant Theory and Enhanced Master Space -- Obstruction Theories of Moduli Stacks and Master Spaces -- Virtual Fundamental Classes -- Invariants.. - 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!
|
| Emner | |
| Dewey | |
| ISBN | 9783540939122
|
