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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Ampleness of intersections of translates of theta divisors in an abelian fourfold


Authors: O. Debarre and E. Izadi
Journal: Proc. Amer. Math. Soc. 135 (2007), 3477-3483
MSC (2000): Primary 14K12; Secondary 14M10, 14F10
Published electronically: June 29, 2007
MathSciNet review: 2336560
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Abstract: We prove the ampleness of the cotangent bundle of the intersection of two general translates of a theta divosor of the Jacobian of a general curve of genus $ 4$. From this, we deduce the same result in a general, principally polarized abelian variety of dimension $ 4$.


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Additional Information

O. Debarre
Affiliation: IRMA – Mathématique, Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg Cedex, France
Email: debarre@math.u-strasbg.fr

E. Izadi
Affiliation: Department of Mathematics, Boyd Graduate Studies Research Center, University of Georgia, Athens, Georgia 30602-7403
Email: izadi@math.uga.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08964-2
PII: S 0002-9939(07)08964-2
Keywords: Ample cotangent bundle, abelian variety, algebraic surface, complete intersection.
Received by editor(s): June 23, 2005
Received by editor(s) in revised form: August 21, 2006
Published electronically: June 29, 2007
Additional Notes: This work was done while O. Debarre was visiting the Department of Mathematics of the University of Georgia, at the invitation of E. Izadi. He is grateful to E. Izadi for her hospitality. Both authors are grateful to the University of Georgia for its support.
Communicated by: Michael Stillman
Article copyright: © Copyright 2007 American Mathematical Society