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arXiv · 1402.4785

Extremal transitions from nested reflexive polytopes

Karl Fredrickson
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Abstract

Using an inclusion of one reflexive polytope into another is a well-known strategy for connecting the moduli spaces of two Calabi-Yau families. In this paper we look at the question of when an inclusion of reflexive polytopes determines a torically-defined extremal transition between smooth Calabi-Yau hypersurface families. We show this is always possible for reflexive polytopes in dimensions two and three. However, in dimension four and higher, obstructions can occur. This leads to a smooth projective family of Calabi-Yau threefolds that is birational to one of Batyrev's hypersurface families, but topologically distinct from all such families.

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Karl Fredrickson. 2014-03-06. Extremal transitions from nested reflexive polytopes. https://doi.org/10.1007/s00220-014-2201-z

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