Extremal transitions from nested reflexive polytopes
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.
Keywords
Cite
@article{arxiv.1402.4785,
title = {Extremal transitions from nested reflexive polytopes},
author = {Karl Fredrickson},
journal= {arXiv preprint arXiv:1402.4785},
year = {2015}
}
Comments
Major change in this version: reworking of section 2 to prove full result in the case of three dimensional reflexive polytopes