Some ball quotients with a Calabi–Yau model
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- by Eberhard Freitag and Riccardo Salvati Manni PDF
- Proc. Amer. Math. Soc. 143 (2015), 3203-3209 Request permission
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 \[ X_0X_1X_2=X_3X_4X_5, X_0^3+X_1^3+X_2^3=X_3^3+X_4^3+X_5^3. \] 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 $72$.References
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Additional Information
- Eberhard Freitag
- Affiliation: Mathematisches Institut, Im Neuenheimer Feld 288, D69120 Heidelberg, Germany
- MR Author ID: 69160
- 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
- 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
- © Copyright 2015 American Mathematical Society
- 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
- MathSciNet review: 3348764