Some Siegel Threefolds with a Calabi-Yau Model II
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In a previous paper, we described some Siegel modular threefolds which admita Calabi-Yau model. Using a different method we give in this paper an enlarged listof such varieties. Basic for this method is a paper of van Geemen and Nygaard. Theystudy a variety X that is the complete intersection of four quadrics in P7(C). This isbiholomorphic equivalent to the Satake compactification of H2/Γ′ for a certain subgroup Γ′ ⊂ Sp(2, Z) and it will be the starting point of our investigation. It has been pointedout that a (projective) small resolution of this variety is a rigid Calabi-Yau manifold ˜X. Then we will consider the action of quotients of modular groups on X and study possibleresolutions that admits a Calabi-Yau model in the category of complex spaces.
Abstract
In a previous paper, we described some Siegel modular threefolds which admita Calabi-Yau model. Using a different method we give in this paper an enlarged listof such varieties. Basic for this method is a paper of van Geemen and Nygaard. Theystudy a variety X that is the complete intersection of four quadrics in P7(C). This isbiholomorphic equivalent to the Satake compactification of H2/Γ′ for a certain subgroup Γ′ ⊂ Sp(2, Z) and it will be the starting point of our investigation. It has been pointedout that a (projective) small resolution of this variety is a rigid Calabi-Yau manifold ˜X. Then we will consider the action of quotients of modular groups on X and study possibleresolutions that admits a Calabi-Yau model in the category of complex spaces.
참고문헌 (14)
- L. Borisov, "On Calabi-Yau threefolds with large nonabelian fundamental groups", Proc. Amer. Math. Soc, 136, pp.1549~1551 (2008)
- W. Bosma, "Magma algebra system. I. The user language", J. Symbolic Comput, 24(3-4), pp.235~265 (1997)
- T. Bridgeland, "The McKay correspondence as an equivalence of derived categories", J. Amer. Math. Soc, 14, pp.535~554 (2001)
- S. Cynk, "Modular Calabi-Yau Threefolds of level eight", Internat. J. Math, 18(3), pp.331~347 (2007)
- S. Cynk, "The geometry and arithmetic of a Calabi-Yau Siegel threefold", Int. Jour. Math, 29, pp.1561~1583 (2011)
- "2009", ~
- E. Freitag, "Some Siegel threefolds with a Calabi-Yau model", Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), pp.833~850 (2010)
- E. Freitag, "Siegelsche Modulfunktionen, Grundlehren der mathematischen Wissenschaften", pp.254~ (1983), Springer
- E. Freitag, "Singular modular forms and theta relations" (1991), Springer-Verlag
- R. Friedmann, "Simultaneous resolution of threefold double points", Mathematische Ann, 274, pp.671~689 (1986)
- J. Kollar, "Flops", Nagoya Math. J, 113, pp.15~36 (1989)
- B. van Geemen, "On the geometry and arithmetic of some Siegel modular threefolds", Journal of Number Theory, 53, pp.45~87 (1995)
- M. Reid, "La correspondence de McKay", S´eminaire Bourbaki 1999, 2002, pp.276 (2000), 53~72
- S. Roan, "Minimal resolutions of Gorenstein orbifolds in dimension three", Topology, 35, pp.489~508 (1996)