The second fundamental form of the moduli space of cubic threefolds in \mathcal A₅

2022/07/27 by Elisabetta Colombo, Paola Frediani, Juan Carlos Naranjo +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Conic section #Geometry #Jacobian matrix and determinant #Kernel (algebra) #Locus (genetics) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Metric (unit) #Moduli space #Pure mathematics #math.AG #msc:14H40 #msc:14J10 #msc:14J30 #msc:32G20

paper · pdf · doi:10.46298/epiga.2023.9962

published as Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (October 27, 2023) epiga:9962

arxiv created 2023/10/26 · openalex publication_date 2023/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01 · arxiv updated 2026/08/05

Abstract

We study the second fundamental form of the Siegel metric in \mathcal A₅ restricted to the locus of intermediate Jacobians of cubic threefolds. We prove that the image of this second fundamental form, which is known to be non-trivial, is contained in the kernel of a suitable multiplication map. Some ingredients are: the conic bundle structure of cubic threefolds, Prym theory, Gaussian maps and Jacobian ideals.

Related

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