Generalized compactifications of Batyrev hypersurface families

TL;DR

This paper introduces a generalized fan-based method for resolving and compactifying Batyrev hypersurface families, resulting in smooth projective Calabi-Yau threefolds that extend beyond traditional MPCP resolutions.

Contribution

It presents a novel approach to compactify Batyrev hypersurfaces using more general fans, enabling smooth projective Calabi-Yau families not achievable with standard methods.

Findings

Generic threefold members are always smooth.

New compactifications extend beyond MPCP resolutions.

Method produces smooth projective Calabi-Yau families.

Abstract

We show how Calabi-Yau hypersurface families arising from Batyrev's construction can be resolved and compactified using a type of fan more general than an MPCP resolution. This can lead to smooth projective compactifications that are not obtainable from the original construction. In the threefold case, we show that generic members of the resulting family are always smooth.