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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
January 2019
|
| In: |
Proceedings of the London Mathematical Society
Year: 2019, Volume: 118, Issue: 1, Pages: 191-220 |
| ISSN: | 1460-244X |
| DOI: | 10.1112/plms.12178 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1112/plms.12178 Verlag, lizenzpflichtig, Volltext: https://onlinelibrary.wiley.com/doi/abs/10.1112/plms.12178 
|
| Author Notes: | Georg Oberdieck, Junliang Shen |
| Summary: | 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. |
|---|---|
| Item Description: | Online veröffentlicht: 2. August 2018 Gesehen am 14.01.2025 |
| Physical Description: | Online Resource |
| ISSN: | 1460-244X |
| DOI: | 10.1112/plms.12178 |