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arXiv · 1612.03102

Reduced Donaldson-Thomas invariants and the ring of dual numbers

Georg Oberdieck·Junliang Shen
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Abstract

Let $A$ be an abelian variety. We introduce $A$-equivariant Grothendieck rings and $A$-equivariant motivic Hall algebras, and endow them with natural integration maps to the ring of dual numbers. The construction allows a systematic treatment of reduced Donaldson-Thomas invariants by Hall algebra techniques. We calculate reduced Donaldson-Thomas invariants for $\mathrm{K3} \times E$ and abelian threefolds for several imprimitive curve classes. This verifies (in special cases) multiple cover formulas conjectured by Oberdieck-Pandharipande and Bryan-Oberdieck-Pandharipande-Yin.

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Georg Oberdieck, Junliang Shen. 2016-12-09. Reduced Donaldson-Thomas invariants and the ring of dual numbers. https://doi.org/10.1112/plms.12178

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