Semistable degenerations of double octics

TL;DR

This paper introduces an algorithm for computing semistable degenerations of double octic Calabi-Yau threefolds, applicable in both complex and arithmetic contexts, demonstrated through explicit examples.

Contribution

It presents a novel combinatorial algorithm for semistable degeneration of double octic Calabi-Yau threefolds, usable over complex and arithmetic settings.

Findings

Successfully computes semistable degenerations for three explicit examples.

Determines limiting mixed Hodge structures for these degenerations.

Demonstrates the algorithm's effectiveness in different mathematical contexts.

Abstract

We present an algorithm for computing semistable degeneration of double octic Calabi-Yau threefolds. Our method has a combinatorial representation by the means of double octic diagrams. The proposed algorithm is applicable both in classical context over a complex disk as well as in arithmetic setting over a spectrum of DVR. We illustrate algorithm's efficacy through three examples where we compute semistable degeneration and limiting mixed Hodge structure for explicit families of double octics.