TY  - BOOK
AU  - Mochizuki,Takuro
ED  - SpringerLink (Online service)
TI  - Donaldson Type Invariants for Algebraic Surfaces: Transition of Moduli Stacks 
T2  - Lecture Notes in Mathematics,
SN  - 9783540939139
AV  - QA564-609 
U1  - 516.35 23
PY  - 2009///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Geometry, algebraic
KW  - Algebraic Geometry
N1  - Preliminaries -- Parabolic L-Bradlow Pairs -- Geometric Invariant Theory and Enhanced Master Space -- Obstruction Theories of Moduli Stacks and Master Spaces -- Virtual Fundamental Classes -- Invariants
N2  - 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!
UR  - https://doi.org/10.1007/978-3-540-93913-9
ER  -