An application of Bogomolov-Gieseker type inequality to counting invariants

Abstract: In this talk, I will work on a smooth projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda, such as the projective space $\mathbb{P}^3$ or the quintic threefold. I will show 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. This is joint work with Richard Thomas

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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