Donaldson Type Invariants for Algebraic Surfaces

Transition of Moduli Stacks

  • Takuro┬áMochizuki

Part of the Lecture Notes in Mathematics book series (LNM, volume 1972)

Table of contents

  1. Front Matter
    Pages 1-20
  2. Takuro Mochizuki
    Pages 1-23
  3. Takuro Mochizuki
    Pages 1-38
  4. Takuro Mochizuki
    Pages 1-33
  5. Takuro Mochizuki
    Pages 1-50
  6. Takuro Mochizuki
    Pages 1-77
  7. Back Matter
    Pages 1-48

About this book


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!


Excel Invariant Natural Obstruction theory Semistable sheaves Smooth function Transition of moduli stacks algebra algebraic surface form invariant theory sheaves

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  • Takuro┬áMochizuki

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