Reduced Donaldson-Thomas invariants and the ring of dual numbers
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 tec...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
January 2019
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| In: |
Proceedings of the London Mathematical Society
Year: 2019, Jahrgang: 118, Heft: 1, Pages: 191-220 |
| ISSN: | 1460-244X |
| DOI: | 10.1112/plms.12178 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1112/plms.12178 Verlag, lizenzpflichtig, Volltext: https://onlinelibrary.wiley.com/doi/abs/10.1112/plms.12178 
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| Verfasserangaben: | Georg Oberdieck, Junliang Shen |
MARC
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| 520 | |a 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 K3×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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