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<p>In this paper we provide applications of general results of Baldi-Klingler-Ullmo and Khelifa-Urbanik on the geometry of the Hodge locus associated to an integral polarized variation of Hodge structures to the case of Noether-Lefschetz loci for families of smooth surfaces. In particular, we consider the family of smooth surfaces in the linear system of a sufficiently ample line bundle on a smooth projective threefold <i>Y</i>, in case <i>Y</i> is a Fano or a Calabi-Yau threefold, and we prove results on the different behaviour of the union of the general, respectively exceptional, components of its Noether-Lefschetz locus.</p>

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Density of Noether–Lefschetz loci for surfaces in Fano and Calabi–Yau threefolds

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  • 发表日期：

    2025年10月29日

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  • Edoardo Mason

摘要

In this paper we provide applications of general results of Baldi-Klingler-Ullmo and Khelifa-Urbanik on the geometry of the Hodge locus associated to an integral polarized variation of Hodge structures to the case of Noether-Lefschetz loci for families of smooth surfaces. In particular, we consider the family of smooth surfaces in the linear system of a sufficiently ample line bundle on a smooth projective threefold Y, in case Y is a Fano or a Calabi-Yau threefold, and we prove results on the different behaviour of the union of the general, respectively exceptional, components of its Noether-Lefschetz locus.