Motivic Donaldson--Thomas invariants of some quantized threefolds

Alberto Cazzaniga, Andrew Morrison, Brent Pym, Balázs Szendroi

Research output: Contribution to journalArticlepeer-review

Abstract

This paper is motivated by the question of how motivic Donaldson--Thomas invariants behave in families. We compute the invariants for some simple families of noncommutative Calabi--Yau threefolds, defined by quivers with homogeneous potentials. These families give deformation quantizations of affine three-space, the resolved conifold, and the resolution of the transversal An-singularity. It turns out that their invariants are generically constant, but jump at special values of the deformation parameter, such as roots of unity. The corresponding generating series are written in closed form, as plethystic exponentials of simple rational functions. While our results are limited by the standard dimensional reduction techniques that we employ, they nevertheless allow us to conjecture formulae for more interesting cases, such as the elliptic Sklyanin algebras.
Original languageEnglish
Pages (from-to)1115-1139
Number of pages19
JournalJournal of Noncommutative Geometry
Volume11
Issue number3
DOIs
Publication statusPublished - 26 Sep 2017

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