(Download) "Donaldson Type Invariants for Algebraic Surfaces" by Takuro Mochizuki * Book PDF Kindle ePub Free
eBook details
- Title: Donaldson Type Invariants for Algebraic Surfaces
- Author : Takuro Mochizuki
- Release Date : January 20, 2009
- Genre: Mathematics,Books,Science & Nature,
- Pages : * pages
- Size : 16018 KB
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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