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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

Introduction

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!

Keywords

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

Authors and affiliations

  • Takuro┬áMochizuki

There are no affiliations available

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-93913-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-93912-2
  • Online ISBN 978-3-540-93913-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site