Soheyla Feyzbakhsh ; Richard P. Thomas - Curve counting and S-duality

epiga:9818 - Épijournal de Géométrie Algébrique, May 12, 2023, Volume 7 - https://doi.org/10.46298/epiga.2023.volume7.9818
Curve counting and S-dualityArticle

Authors: Soheyla Feyzbakhsh ; Richard P. Thomas ORCID

    We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda, such as $\mathbb P^3$ or the quintic threefold. We prove certain moduli spaces of 2-dimensional torsion sheaves on $X$ are smooth bundles over Hilbert schemes of ideal sheaves of curves and points in $X$. When $X$ is Calabi-Yau this gives a simple wall crossing formula expressing curve counts (and so ultimately Gromov-Witten invariants) in terms of counts of D4-D2-D0 branes. These latter invariants are predicted to have modular properties which we discuss from the point of view of S-duality and Noether-Lefschetz theory.


    Volume: Volume 7
    Published on: May 12, 2023
    Accepted on: February 7, 2023
    Submitted on: July 21, 2022
    Keywords: Mathematics - Algebraic Geometry,High Energy Physics - Theory,14N35, 14D20, 14J60, 14F05
    Funding:
      Source : OpenAIRE Graph
    • Derived categories, stability conditions and geometric applications.; Funder: UK Research and Innovation; Code: EP/T018658/1
    • Vafa-Witten invariants of projective surfaces; Funder: UK Research and Innovation; Code: EP/R013349/1

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