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Donaldson Type Invariants for Algebraic Surfaces

Transition of Moduli Stacks

  • Book
  • © 2009

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Authors:
  1. Takuro Mochizuki
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1972)

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Table of contents (7 chapters)

  1. Front Matter

    Pages 1-20
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  2. Introduction

    • Takuro Mochizuki
    Pages 1-23

  3. Preliminaries

    • Takuro Mochizuki
    Pages 1-38

  4. Parabolic L-Bradlow Pairs

    • Takuro Mochizuki
    Pages 1-33

  5. Geometric Invariant Theory and Enhanced Master Space

    • Takuro Mochizuki
    Pages 1-47

  6. Obstruction Theories of Moduli Stacks and Master Spaces

    • Takuro Mochizuki
    Pages 1-67

  7. Virtual Fundamental Classes

    • Takuro Mochizuki
    Pages 1-50

  8. Invariants

    • Takuro Mochizuki
    Pages 1-77

  9. Back Matter

    Pages 1-48
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Keywords

About this book

In this monograph, we de?ne and investigate an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface. We may expect the existence of interesting “universal relations among invariants”, which would be a natural generalization of the “wall-crossing formula” and the “Witten conjecture” for classical Donaldson invariants. Our goal is to obtain a weaker version of such relations, in other brief words, to describe a relation as the sum of integrals over the products of m- uli spaces of objects with lower ranks. Fortunately, according to a recent excellent work of L. Gottsche, ¨ H. Nakajima and K. Yoshioka, [53], a wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case. We hope that our work in this monograph would, at least tentatively, provides a part of foundation for the further study on such universal relations. In the rest of this preface, we would like to explain our motivation and some of important ingredients of this study. See Introduction for our actual problems and results. Donaldson Invariants Let us brie?y recall Donaldson invariants. We refer to [22] for more details and precise. We also refer to [37], [39], [51] and [53]. LetX be a compact simply con- ? nected oriented real 4-dimensional C -manifold with a Riemannian metric g. Let P be a principalSO(3)-bundle on X.

Bibliographic Information

  • Book Title: Donaldson Type Invariants for Algebraic Surfaces

  • Book Subtitle: Transition of Moduli Stacks

  • Authors: Takuro Mochizuki

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-540-93913-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2009

  • Softcover ISBN: 978-3-540-93912-2Published: 27 March 2009

  • eBook ISBN: 978-3-540-93913-9Published: 20 April 2009

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XXIII, 383

  • Topics: Algebraic Geometry

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