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arXiv · 1211.2390

New examples of Calabi-Yau threefolds and genus zero surfaces

Gilberto Bini·Filippo F. Favale·Jorge Neves·Roberto Pignatelli
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Abstract

We classify the subgroups of the automorphism group of the product of 4 projective lines admitting an invariant anticanonical smooth divisor on which the action is free. As a first application, we describe new examples of Calabi-Yau 3-folds with small Hodge numbers. In particular, the Picard number is 1 and the number of moduli is 5. Furthermore, the fundamental group is non-trivial. We also construct a new family of minimal surfaces of general type with geometric genus zero, K^2=3 and fundamental group of order 16. We show that this family dominates an irreducible component of dimension 4 of the moduli space of the surfaces of general type.

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Gilberto Bini, Filippo F. Favale, Jorge Neves, Roberto Pignatelli. 2013-02-18. New examples of Calabi-Yau threefolds and genus zero surfaces. https://doi.org/10.1142/s0219199713500107

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