Advanced Studies in Pure Mathematics

From GW invariants of symmetric product stacks to relative invariants of threefolds

Wan Keng Cheong

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Abstract

In this note, we relate the equivariant GW invariants of the symmetric product stacks of any nonsingular toric surface $X$ in genus zero to the equivariant relative GW invariants of the threefold $X \times \mathbb{P}^1$ in all genera. We give an example for which an equivalence between these two theories exists.

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), 59-81

Dates
Received: 23 December 2011
Revised: 1 June 2012
First available in Project Euclid: 19 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1539916446

Digital Object Identifier
doi:10.2969/aspm/06510059

Mathematical Reviews number (MathSciNet)
MR3380775

Zentralblatt MATH identifier
1360.14128

Subjects
Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]

Keywords
Orbifold Gromov–Witten invariant symmetric product stack relative Gromov–Witten invariant

Citation

Cheong, Wan Keng. From GW invariants of symmetric product stacks to relative invariants of threefolds. Algebraic Geometry in East Asia — Taipei 2011, 59--81, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06510059. https://projecteuclid.org/euclid.aspm/1539916446


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