arXiv subjects

Marcin Oczko

Publications and source records attributed to Marcin Oczko.

2 recordsLinked to original sources

arXiv2025

Semistable degenerations of double octics

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.

math.AG↗

arXiv2024

Counterexample to Néron-Ogg-Shafarevich criterion for Calabi-Yau threefolds

For any prime $p>5$ we construct a Calabi-Yau threefold $X$ defined over a finite extension $K$ of $\mathbb{Q}_p$ such that every model of $X$ over $\operatorname{Spec}\mathcal{O}_K$ has singular special fiber, yet the Galois action on the $\ell$-adic cohomology group $H^3_{\acute{e}t}(X,\mathbb{Q}_\ell)$ is unramified for $\ell\neq p$ and crystalline for $\ell=p$. This provides a counterexample to the analogue of the Néron-Ogg-Shafarevich criterion for three-dimensional Calabi-Yau manifolds.

math.AG↗