General infinitesimal variations of the Hodge structure of ample curves in surfaces

Víctor González‐Alonso and Sara Torelli

Mathematische Nachrichten, 2025, vol. 298, issue 7, 2282-2308

Abstract: Given a smooth projective complex curve inside a smooth projective surface, one can ask how its Hodge structure varies when the curve moves inside the surface. In this paper, we develop a general theory to study the infinitesimal version of this question in the case of ample curves. We can then apply the machinery to show that the infinitesimal variation of the Hodge structure of a general deformation of an ample curve in P1×P1$\mathbb {P}^1\times \mathbb {P}^1$ is an isomorphism.

Date: 2025
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https://doi.org/10.1002/mana.12028

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