- Abstract:
-
We prove that the GW theory of negative line bundles M = Tot(L→B) determines the symplectic cohomology: indeed SH *(M) is the quotient of QH *(M) by the kernel of a power of quantum cup product by c1(L). We prove this also for negative vector bundles and the top Chern class. We calculate SH * and QH * for O(-n)→CPm. For example: for O(-1), M is the blow-up of Cm+1 at the origin and SH *(M) has rank m. We prove Kodaira vanishing: for very negative L, SH * = 0; and Serre vanishing: if we twist ...
Expand abstract - Publisher copy:
- 10.1016/j.aim.2014.06.009
-
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- Publisher:
- Academic Press Inc.
- Journal:
- Advances in Mathematics
- Volume:
- 262
- Pages:
- 1035-1106
- Publication date:
- 2014-09-10
- DOI:
- EISSN:
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1090-2082
- ISSN:
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0001-8708
- URN:
-
uuid:ece26f01-ae15-45c6-81de-9317985d7cc7
- Source identifiers:
-
369649
- Local pid:
- pubs:369649
- Language:
- English
- Keywords:
- Copyright date:
- 2014
Journal article
Floer theory for negative line bundles via Gromov-Witten invariants
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