Donaldson-Thomas theory of the quantum Fermat quintic

Moduli and Algebraic Cycles

05 October 14:30 - 15:30

Kai Behrend - University of British Columbia

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 up to carefully chosen 5th roots of unity. We explore the moduli theory of finite length modules, which mixes features of the Hilbert scheme of commutative 3-folds, and the representation theory of quivers with potential. This is mostly work of Yu-Hsiang Liu, with contributions by myself and Atsushi Kanazawa.

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John Christian Ottem
University of Oslo
Dan Petersen
Stockholm University
David Rydh
KTH Royal Institute of Technology


Dan Petersen


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