Integrality of relative BPS state counts of toric Del Pezzo surfaces
Event details
| Date | 17.01.2014 |
| Hour | 13:00 › 14:00 |
| Speaker | Michel van Garrel (University of Alberta) |
| Location | |
| Category | Conferences - Seminars |
Abstract :
Relative BPS state counts for log Calabi-Yau surface pairs were introduced by Gross-Pandharipande-Siebert and conjectured by the authors to be integers. For toric Del Pezzo surfaces, we provide an arithmetic proof of this conjecture, by relating these invariants to the local BPS state counts of the surfaces. The latter were shown to be integers by Peng; and more generally for toric Calabi-Yau threefolds by Konishi. Local BPS state counts were computed by Chiang-Klemm-Yau-Zaslow via local mirror symmetry. Analogously, relative BPS state counts are related to log mirror symmetry, which for the projective plane was developed by Takahashi. Relative BPS state counts are an intrinsic (virtual) extension of the A-model invariants considered by Takahashi. The relative BPS state counts satisfy an adapted log mirror symmetry conjecture by Takahashi: they are linearly related to the local BPS state counts and are thus calculated by periods of the mirror family.
Relative BPS state counts for log Calabi-Yau surface pairs were introduced by Gross-Pandharipande-Siebert and conjectured by the authors to be integers. For toric Del Pezzo surfaces, we provide an arithmetic proof of this conjecture, by relating these invariants to the local BPS state counts of the surfaces. The latter were shown to be integers by Peng; and more generally for toric Calabi-Yau threefolds by Konishi. Local BPS state counts were computed by Chiang-Klemm-Yau-Zaslow via local mirror symmetry. Analogously, relative BPS state counts are related to log mirror symmetry, which for the projective plane was developed by Takahashi. Relative BPS state counts are an intrinsic (virtual) extension of the A-model invariants considered by Takahashi. The relative BPS state counts satisfy an adapted log mirror symmetry conjecture by Takahashi: they are linearly related to the local BPS state counts and are thus calculated by periods of the mirror family.
Practical information
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Contact
- Monique Kiener