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Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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

Author(s): Andreas Leopold Knutsen; Angelo Felice Lopez
Journal: Proc. Amer. Math. Soc. 135 (2007), 3495-3498.
MSC (2000): Primary 14F17, 14J28; Secondary 14C20
Posted: July 3, 2007
MathSciNet review: 2336562
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Abstract | References | Similar articles | Additional information

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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F. R. Cossec, I. V. Dolgachev. Enriques Surfaces I. Progress in Mathematics 76. Birkhäuser Boston, MA, 1989. MR 986969 (90h:14052)

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F. R. Cossec. Projective models of Enriques surfaces. Math. Ann. 265 (1983), 283-334. MR 721398 (86d:14035)

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Y. Kawamata. A generalization of Kodaira-Ramanujam's vanishing theorem. Math. Ann. 261 (1982), 43-46. MR 675204 (84i:14022)

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T. Johnsen, A. L. Knutsen. $ K3$ projective models in scrolls. Lecture Notes in Mathematics 1842. Springer-Verlag, Berlin, 2004. MR 2067777 (2005g:14074)

[KL1]
A. L. Knutsen, A. F. Lopez. Brill-Noether theory of curves on Enriques surfaces I: the positive cone and gonality. Preprint 2006.

[KL2]
A. L. Knutsen, A. F. Lopez. Brill-Noether theory of curves on Enriques surfaces II. In preparation.

[KL3]
A. L. Knutsen, A. F. Lopez. Surjectivity of Gaussian maps for curves on Enriques surfaces. Adv. Geom. 7 (2007), 215-267.

[KLM]
A. L. Knutsen, A. F. Lopez, R. Muñoz. On the extendability of projective surfaces and a genus bound for Enriques-Fano threefolds. Preprint 2006.

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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: 10.1090/S0002-9939-07-08968-X
PII: S 0002-9939(07)08968-X
Received by editor(s): December 15, 2005
Received by editor(s) in revised form: August 22, 2006
Posted: 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 of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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