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<p>We provide examples of smooth three-dimensional Fano complete intersections of degree 2,&#xa0;4,&#xa0;6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute coregularity zero.</p>

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On smooth Fano threefolds with coregularity zero

  • 期刊论文

  • 发表日期：

    2025年11月23日

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  • Olzhas Zhakupov

摘要

We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute coregularity zero.