Reduced Donaldson–Thomas invariants and the ring of dual numbers
G Oberdieck, J Shen - Proceedings of the London …, 2019 - Wiley Online Library
Proceedings of the London Mathematical Society, 2019•Wiley Online Library
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 (DT) invariants by Hall algebra techniques. We calculate reduced DT invariants for
K 3× E and abelian threefolds for several imprimitive curve classes. This verifies (in special
cases) multiple cover formulas conjectured by Oberdieck–Pandharipande and Bryan …
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 (DT) invariants by Hall algebra techniques. We calculate reduced DT invariants for
K 3× E and abelian threefolds for several imprimitive curve classes. This verifies (in special
cases) multiple cover formulas conjectured by Oberdieck–Pandharipande and Bryan …
Abstract
Let be an abelian variety. We introduce ‐equivariant Grothendieck rings and ‐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 (DT) invariants by Hall algebra techniques. We calculate reduced DT invariants for 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.
Wiley Online Library