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Donaldson-Thomas theory of non-commutative projective schemes

Banff International Research Station for Mathematical Innovation and Discovery

We study non-commutative projective varieties in the sense of Artin-Zhang, which are given by non-commutative homogeneous coordinate rings, which are finite over their centre. We construct moduli spaces of stable modules for these, and construct a symmetric obstruction theory in the CY3-case. This gives deformation invariants of Donaldson-Thomas type. The simplest example is the Fermat quintic in quantum projective space, where the coordinates commute only up to carefully chosen 5th roots of unity. We explore the moduli theory of finite length modules, which mixes features both of the Hilbert scheme of commutative 3-folds, and the representation theory of quivers with potential. This is mostly a report on the work of Yu-Hsiang Liu, with contributions by myself and Atsushi Kanazawa.

Mathematics; Algebraic geometry

video/mp4

Author affiliation: University of British Columbia

2020-05-17

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/74495

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/