A sharp vanishing theorem for line bundles on K3 or Enriques surfaces
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- by Andreas Leopold Knutsen and Angelo Felice Lopez PDF
- Proc. Amer. Math. Soc. 135 (2007), 3495-3498 Request permission
Abstract:
Let $L$ be a line bundle on a K3 or Enriques surface. We give a vanishing theorem for $H^1(L)$ that, unlike most vanishing theorems, gives necessary and sufficient geometrical conditions for the vanishing. This result is essential in our study of Brill-Noether theory of curves on Enriques surfaces (2006) and of Enriques-Fano threefolds (2006 preprint).References
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Additional Information
- Andreas Leopold Knutsen
- Affiliation: Dipartimento di Matematica, Università di Roma Tre, Largo San Leonardo Murialdo 1, 00146, Roma, Italy
- MR Author ID: 676183
- Email: knutsen@mat.uniroma3.it
- Angelo Felice Lopez
- Affiliation: Dipartimento di Matematica, Università di Roma Tre, Largo San Leonardo Murialdo 1, 00146, Roma, Italy
- MR Author ID: 289566
- ORCID: 0000-0003-4923-6885
- Email: lopez@mat.uniroma3.it
- Received by editor(s): December 15, 2005
- Received by editor(s) in revised form: August 22, 2006
- Published electronically: July 3, 2007
- Additional Notes: The research of the first author was partially supported by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Programme
The research of the second author was partially supported by the MIUR national project “Geometria delle varietà algebriche” COFIN 2002-2004. - Communicated by: Michael Stillman
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3495-3498
- MSC (2000): Primary 14F17, 14J28; Secondary 14C20
- DOI: https://doi.org/10.1090/S0002-9939-07-08968-X
- MathSciNet review: 2336562