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Zero-dimensional Donaldson-Thomas invariants of Calabi-Yau fourfolds

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Speaker: 
Martijn Kool
Affiliation: 
Utrecht)
Date: 
Thu, 2018-12-06 10:30 - 12:00
Location: 
MPIM Lecture Hall

The Hilbert scheme of n points on a Calabi-Yau fourfold carries a virtual cycle of degree n constructed by Borisov-Joyce. I present a conjectural formula for the invariants obtained by capping the virtual cycle with the top Chern class of a tautological bundle. I discuss evidence for this conjecture by considering (1) small numbers of points and (2) toric fourfolds. For affine four-space, this implies a conjecture about solid partitions. The latter is a specialization of a recent conjecture on solid partitions derived in physics by N. Nekrasov. Joint work with Y. Cao.

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