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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Calabi-Yau three-folds and moduli of abelian surfaces II
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by Mark Gross and Sorin Popescu PDF
Trans. Amer. Math. Soc. 363 (2011), 3573-3599 Request permission


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
  • Email:
  • 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
  • Email:
  • 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.
  • © Copyright 2011 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 3573-3599
  • MSC (2000): Primary 14K10, 14J32
  • DOI:
  • MathSciNet review: 2775819