Takuro Mochizuki

Donaldson Type Invariants for Algebraic Surfaces (eBook, PDF)

Transition of Moduli Stacks

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 383
• Erscheinungstermin: 20. April 2009
• Englisch
• ISBN-13: 9783540939139
• Artikelnr.: 44226682

Inhaltsangabe

Preliminaries.- Parabolic L-Bradlow Pairs.- Geometric Invariant Theory and Enhanced Master Space.- Obstruction Theories of Moduli Stacks and Master Spaces.- Virtual Fundamental Classes.- Invariants.