Advanced Studies in Pure Mathematics

ADHM sheaf theory and wallcrossing

Wu-yen Chuang

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Abstract

In this article we survey the recent developments in ADHM sheaf theory on a smooth projective variety $X$. When $X$ is a curve the theory is an alternative construction of stable pair theory of Pandharipande and Thomas or Gromov–Witten theory on local curve geometries. The construction relies on relative Beilinson spectral sequence and Fourier–Mukai transformation. We will present some applications of the theory, including the derivations of the wallcrossing formulas, higher rank Donaldson–Thomas invariants on local curves, and the coholomogies of the moduli of stable Hitchin pairs.

Article information

Source
Algebraic Geometry in East Asia — Taipei 2011, J. A. Chen, M. Chen, Y. Kawamata and J. Keum, eds. (Tokyo: Mathematical Society of Japan, 2015), 83-106

Dates
Received: 27 December 2011
Revised: 6 August 2012
First available in Project Euclid: 19 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1539916447

Digital Object Identifier
doi:10.2969/aspm/06510083

Mathematical Reviews number (MathSciNet)
MR3380776

Zentralblatt MATH identifier
1360.14129

Subjects
Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 81T30: String and superstring theories; other extended objects (e.g., branes) [See also 83E30]

Keywords
Generalized Donaldson–Thomas invariants ADHM sheaf theory wallcrossing formulas

Citation

Chuang, Wu-yen. ADHM sheaf theory and wallcrossing. Algebraic Geometry in East Asia — Taipei 2011, 83--106, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06510083. https://projecteuclid.org/euclid.aspm/1539916447


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