Lecture Notes in Mathematics
cover

Donaldson Type Invariants for Algebraic Surfaces

Transition of Moduli Stacks

Authors: Mochizuki, Takuro

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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!

Table of contents (7 chapters)

Table of contents (7 chapters)
  • Introduction

    Mochizuki, Takuro

    Pages 1-23

  • Preliminaries

    Mochizuki, Takuro

    Pages 1-38

  • Parabolic L-Bradlow Pairs

    Mochizuki, Takuro

    Pages 1-33

  • Geometric Invariant Theory and Enhanced Master Space

    Mochizuki, Takuro

    Pages 1-47

  • Obstruction Theories of Moduli Stacks and Master Spaces

    Mochizuki, Takuro

    Pages 1-67

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-540-93913-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.99
price for USA in USD
  • ISBN 978-3-540-93912-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Donaldson Type Invariants for Algebraic Surfaces
Book Subtitle
Transition of Moduli Stacks
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1972
Copyright
2009
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-93913-9
DOI
10.1007/978-3-540-93913-9
Softcover ISBN
978-3-540-93912-2
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XXIII, 383
Topics