We study the Hulek-Verril families of Calabi-Yau threefolds[4, 5]. They are birationally equivalent to fibred products of elliptic surfaces so we expect to be able to compute periods on these threefolds by integrating products of elliptic periods over a contour on a ℙ1. We numerically verify this in several examples. The Hulek-Verril threefolds are interesting because some of them are attractor varieties of rank two. These are modular threefolds where the Hodge structure splits over the rational numbers in a specific way. This note is part of an ongoing effort to better understand attractor varieties of rank two.

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Some identities for periods of Hulek-Verrill threefolds

  • Xenia de la Ossa,
  • Mohamed Elmi

摘要

We study the Hulek-Verril families of Calabi-Yau threefolds[4, 5]. They are birationally equivalent to fibred products of elliptic surfaces so we expect to be able to compute periods on these threefolds by integrating products of elliptic periods over a contour on a ℙ1. We numerically verify this in several examples. The Hulek-Verril threefolds are interesting because some of them are attractor varieties of rank two. These are modular threefolds where the Hodge structure splits over the rational numbers in a specific way. This note is part of an ongoing effort to better understand attractor varieties of rank two.