In a previous paper, we described some Siegel modular threefolds which admit a Calabi-Yau model. Using a different method we give in this paper an enlarged list of such varieties. Basic for this method is a paper of van Geemen and Nygaard. They study a variety \calX that is the complete intersection of four quadrics in \PP7(\CC). This is biholomorphic equivalent to the Satake compactification of \calH2/Γ′ for a certain subgroup Γ′⊂\Sp(2,\ZZ) and it will be the starting point of our investigation. It has been pointed out that a (projective) small resolution of this variety is a rigid Calabi-Yau manifold \calX~. Then we will consider the action of quotients of modular groups on \calX and study possible resolutions that admits a Calabi-Yau model in the category of complex spaces.
In a previous paper, we described some Siegel modular threefolds which admit a Calabi-Yau model. Using a different method we give in this paper an enlarged list of such varieties. Basic for this method is a paper of van Geemen and Nygaard. They study a variety X that is the complete intersection of four quadrics in P7(C). This is biholomorphic 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 pointed out that a (projective) small resolution of this variety is a rigid Calabi-Yau manifold X̄. Then we will consider the action of quotients of modular groups on X and study possible resolutions that admits a Calabi-Yau model in the category of complex spaces.
Some Siegel threefolds with a Calabi-Yau model II / Eberhard, Freitag; SALVATI MANNI, Riccardo. - In: KYUNGPOOK MATHEMATICAL JOURNAL. - ISSN 1225-6951. - STAMPA. - 53:2(2013), pp. 149-174. [10.5666/kmj.2013.53.2.149]
Some Siegel threefolds with a Calabi-Yau model II
SALVATI MANNI, Riccardo
2013
Abstract
In a previous paper, we described some Siegel modular threefolds which admit a Calabi-Yau model. Using a different method we give in this paper an enlarged list of such varieties. Basic for this method is a paper of van Geemen and Nygaard. They study a variety \calX that is the complete intersection of four quadrics in \PP7(\CC). This is biholomorphic equivalent to the Satake compactification of \calH2/Γ′ for a certain subgroup Γ′⊂\Sp(2,\ZZ) and it will be the starting point of our investigation. It has been pointed out that a (projective) small resolution of this variety is a rigid Calabi-Yau manifold \calX~. Then we will consider the action of quotients of modular groups on \calX and study possible resolutions that admits a Calabi-Yau model in the category of complex spaces.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
