Orientation on moduli spaces of sheaves on a non-compact Calabi–Yau 4-fold

08.11.2019 11:15 - 12:15

Arkadij Bojko (Oxford University)

Abstract:

An important part of obtaining a virtual fundamental cycle in enumerative geometry is constructing the orientation on the moduli space. For a non-compact Calabi–Yau 4-fold, one can wish to compute Donaldson–Thomas-type invariants “counting” compactly supported semi-stable sheaves by integrating
 against the virtual fundamental cycle. As such, there is a need for a notion of an orientation bundle on the higher moduli stack of perfect complexes.
In the talk, we will define such an orientation bundle. We show that it is trivial when there exists a spin compactification and give examples.

Organiser:
G. Dimitrov und A. Mellit
Location:

SR 09, 2. OG, OMP 1