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Some ball quotients with a Calabi-Yau model


Authors: Eberhard Freitag and Riccardo Salvati Manni
Journal: Proc. Amer. Math. Soc. 143 (2015), 3203-3209
MSC (2010): Primary 11F46; Secondary 14J32
DOI: https://doi.org/10.1090/S0002-9939-2015-11975-2
Published electronically: March 24, 2015
MathSciNet review: 3348764
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Abstract: Recently we determined explicitly a Picard modular variety of general type. On the regular locus of this variety there are holomorphic three forms which have been constructed as Borcherds products. Resolutions of quotients of this variety, such that the zero divisors are in the branch locus, are candidates for Calabi-Yau manifolds. Here we treat one distinguished example for this. In fact we shall recover a known variety given by the equations

$\displaystyle X_0X_1X_2=X_3X_4X_5, \,\, X_0^3+X_1^3+X_2^3=X_3^3+X_4^3+X_5^3. $

as a Picard modular variety. This variety has a projective small resolution which is a rigid Calabi-Yau manifold ($ h^{12}=0$) with Euler number $ 72$.


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Additional Information

Eberhard Freitag
Affiliation: Mathematisches Institut, Im Neuenheimer Feld 288, D69120 Heidelberg, Germany
Email: freitag@mathi.uni-heidelberg.de

Riccardo Salvati Manni
Affiliation: Universitá di Roma, Piazzale Aldo Moro, 2, I-00185 Roma, Italy
Email: salvati@mat.uniroma1.it

DOI: https://doi.org/10.1090/S0002-9939-2015-11975-2
Received by editor(s): May 24, 2012
Received by editor(s) in revised form: July 28, 2012
Published electronically: March 24, 2015
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2015 American Mathematical Society