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    Talks and Seminars

    SAG: Vafa-Witten invariants and framed sheavesSeminar Algebraic Geometry (SAG)

    by Noah Arbesfeld (Utrecht)

    → Europe/Berlin
    MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

    MPIM, Vivatsgasse, 7 - Lecture Hall

    Max Planck Institute for Mathematics

    120
    Description

    Tanaka-Thomas?s algebro-geometric approach to Vafa-Witten theory defines invariants of projective surfaces using moduli spaces of stable Higgs pairs. I will present work with M. Kool and T. Laarakker, in which we express certain Vafa-Witten invariants in terms of the equivariant geometry of a quiver variety, the moduli space of torsion-free framed sheaves on P^2. I'll then present wall-crossing results for this moduli space of framed sheaves and extract consequences for Vafa-Witten invariants, including a formula for so-called "vertical" Vafa-Witten invariants in rank 2.