Semistable degenerations of double octics

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.