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<p>We present an algorithm for computing semistable degenerations of one-parameter families of double octic Calabi-Yau threefolds. The proposed algorithm is applicable both in the classical context over the complex disk as well as in the arithmetic setting over the spectrum of a discrete valuation ring. We demonstrate the efficiency of our algorithm through three examples of explicit families of double octics, for which we compute semistable degenerations and derive the limiting mixed Hodge structures. Our method has a combinatorial representation by means of double octic diagrams.</p>

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Semistable degenerations of double octics

  • 期刊论文

  • 发表日期：

    2026年2月19日

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  • Marcin Oczko

摘要

We present an algorithm for computing semistable degenerations of one-parameter families of double octic Calabi-Yau threefolds. The proposed algorithm is applicable both in the classical context over the complex disk as well as in the arithmetic setting over the spectrum of a discrete valuation ring. We demonstrate the efficiency of our algorithm through three examples of explicit families of double octics, for which we compute semistable degenerations and derive the limiting mixed Hodge structures. Our method has a combinatorial representation by means of double octic diagrams.