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Transactions of the American Mathematical Society

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Calabi-Yau three-folds and moduli of abelian surfaces II

Authors: Mark Gross and Sorin Popescu
Journal: Trans. Amer. Math. Soc. 363 (2011), 3573-3599
MSC (2000): Primary 14K10, 14J32
Published electronically: January 28, 2011
MathSciNet review: 2775819
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Abstract: We give explicit descriptions of the moduli spaces of abelian surfaces with polarizations of type $(1,d)$, for $d=12,14,16,18$ and $20$. More precisely, in each case we show that a certain choice of moduli space of such abelian surfaces with a partial level structure can be described explicitly and is unirational, and in some cases rational. These moduli spaces with partial level structure are covers of the ordinary moduli spaces, so the Kodaira dimension of the ordinary moduli spaces in these cases is $-\infty$. In addition, we give a few new examples of Calabi-Yau three-folds fibred in abelian surfaces. In the case of $d=20$, such Calabi-Yau three-folds play a key role in the description of the abelian surfaces.

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Additional Information

Mark Gross
Affiliation: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112
MR Author ID: 308804

Sorin Popescu
Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794-3651
Address at time of publication: Renaissance Technologies, 600 Route 25A, East Setauket, New York 11733

Received by editor(s): April 21, 2009
Received by editor(s) in revised form: August 4, 2009
Published electronically: January 28, 2011
Additional Notes: This work was partially supported by NSF grants DMS-0805328, DMS-0502070, DMS-0083361, and MSRI, Berkeley.
Article copyright: © Copyright 2011 American Mathematical Society