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Mathematics > Complex Variables

arXiv:1001.5312 (math)
This paper has been withdrawn by Atsuhira Nagano
[Submitted on 29 Jan 2010 (v1), last revised 29 Mar 2016 (this version, v5)]

Title:Period differential equations for families of K3 surfaces derived from some 3 dimensional reflexive polytopes

Authors:Atsuhira Nagano
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Abstract:We study period maps for families of $K3$ surfaces those are given by anti canonical divisors of toric varieties coming from reflexive polytopes $P_2, P_4, P_5$ and $P_r$. We obtain systems of period differential equations for these families. Moreover, in the case $P_4$, we determine the projective monodromy group of the period map. This group is explicitly related with the Hilbert modular group for $\mathbb{Q}(\sqrt{5})$.
Comments: The results of this paper are contained in "Period differential equations for the families of K3 surfaces with 2 parameters derived from the reflexive polytopes "
Subjects: Complex Variables (math.CV)
Cite as: arXiv:1001.5312 [math.CV]
  (or arXiv:1001.5312v5 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1001.5312

Submission history

From: Atsuhira Nagano [view email]
[v1] Fri, 29 Jan 2010 02:18:40 UTC (42 KB)
[v2] Mon, 15 Feb 2010 04:41:46 UTC (43 KB)
[v3] Fri, 23 Apr 2010 08:39:42 UTC (44 KB)
[v4] Wed, 1 Dec 2010 10:56:51 UTC (1 KB) (withdrawn)
[v5] Tue, 29 Mar 2016 13:21:58 UTC (1 KB) (withdrawn)
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