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Seminar of Algebraic Geometry in East Asia
 
16:15 - 17:15, February 19, 2021 (Friday)
broadcast in Room 515, Cosmology Bldg., Online seminar
(線上演講 於宇宙學大樓515教室收播)
An Application of a Bogomolov-Gieseker Type Inequality to Counting Invariants
Soheyla Feyzbakhsh (Imperial College London)

Abstract:

In this talk, I will work on a smooth projective threefold X which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-Toda, such as the projective space 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 isjoint work with Richard Thomas.

 

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