Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

The primitive cohomology of the theta divisor of an abelian fivefold


Authors: E. Izadi, Cs. Tamás and J. Wang
Journal: J. Algebraic Geom. 26 (2017), 107-175
DOI: https://doi.org/10.1090/jag/679
Published electronically: June 28, 2016
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Abstract | References | Additional Information

Abstract: The primitive cohomology of the theta divisor of a principally polarized abelian variety of dimension $ g$ contains a Hodge structure of level $ g-3$ which we call the primal cohomology. The Hodge conjecture predicts that this is contained in the image, under the Abel-Jacobi map, of the cohomology of a family of curves in the theta divisor. In this paper we use the Prym map to show that this version of the Hodge conjecture is true for the theta divisor of a general abelian fivefold.


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Additional Information

E. Izadi
Affiliation: Department of Mathematics, University of California San Diego, 9500 Gilman Drive #0112, La Jolla, California 92093-0112
Email: eizadi@math.ucsd.edu

Cs. Tamás
Affiliation: Department of Mathematics and Statistics, Langara College, 100 West 49th Avenue, Vancouver, BC, Canada V5Y 2Z6
Email: ctamas@langara.bc.ca

J. Wang
Affiliation: Department of Mathematics, University of California San Diego, 9500 Gilman Drive #0112, La Jolla, California 92093-0112
Email: jiewang884@gmail.com

DOI: https://doi.org/10.1090/jag/679
Received by editor(s): December 24, 2013
Received by editor(s) in revised form: November 1, 2014
Published electronically: June 28, 2016
Additional Notes: The authors are indebted to the referees for a careful reading of this manuscript and many helpful comments and suggestions. The first author was partially supported by the National Science Foundation and the National Security Agency. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF or NSA
Dedicated: Dedicated to Herb Clemens
Article copyright: © Copyright 2016 University Press, Inc.

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