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A sharp vanishing theorem for line bundles on K3 or Enriques surfaces


Authors: Andreas Leopold Knutsen and Angelo Felice Lopez
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
Published electronically: July 3, 2007
MathSciNet review: 2336562
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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).


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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
Email: knutsen@mat.uniroma3.it

Angelo Felice Lopez
Affiliation: Dipartimento di Matematica, Università di Roma Tre, Largo San Leonardo Murialdo 1, 00146, Roma, Italy
Email: lopez@mat.uniroma3.it

DOI: https://doi.org/10.1090/S0002-9939-07-08968-X
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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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