Donaldson Type Invariants for Algebraic Surfaces
Mochizuki, Takuro.
Donaldson Type Invariants for Algebraic Surfaces Transition of Moduli Stacks / [electronic resource] : by Takuro Mochizuki. - XXIII, 383 p. online resource. - Lecture Notes in Mathematics, 1972 0075-8434 ; . - Lecture Notes in Mathematics, 1972 .
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!
9783540939139
10.1007/978-3-540-93913-9 doi
Geometry, algebraic.
Algebraic Geometry.
QA564-609
516.35
Donaldson Type Invariants for Algebraic Surfaces Transition of Moduli Stacks / [electronic resource] : by Takuro Mochizuki. - XXIII, 383 p. online resource. - Lecture Notes in Mathematics, 1972 0075-8434 ; . - Lecture Notes in Mathematics, 1972 .
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!
9783540939139
10.1007/978-3-540-93913-9 doi
Geometry, algebraic.
Algebraic Geometry.
QA564-609
516.35