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Counting sheaves by counting curves

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Richard Thomas
Imperial College London
Thu, 01/12/2022 - 10:30 - 12:00
MPIM Lecture Hall

Contact: Prof. D. Huybrechts.

DT invariants count stable bundles and sheaves on a Calabi-Yau 3-fold X. The generalised DT invariants of Joyce-Song count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants counting ideal sheaves of curves in X. By the MNOP conjecture the latter invariants are determined by the Gromov-Witten invariants of X. Along the way we also show all these invariants are determined by rank 0 invariants counting sheaves supported on surfaces in X. These invariants are predicted by S-duality to be governed by (vector-valued, mock) modular forms.

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