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arxiv: 2501.10192 · v2 · pith:7QSH2GIOnew · submitted 2025-01-17 · 🧮 math.AG

Lefschetz Defect in Families

classification 🧮 math.AG
keywords defectlefschetzsmoothfamiliesvarietyabeliancharacterizationcharacterize
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We provide a cohomological characterization of the Lefschetz defect of smooth complex projective varieties. As a consequence, we deduce that the Lefschetz defect of a smooth Fano variety is invariant under smooth deformation. We also characterize the Lefschetz defect of an abelian variety in terms of its isogeny factors, and study it in families.

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