On the local geometry of the moduli space of (2,2)-threefolds in \mathcal A₉

2023/10/16 by Colombo, Elisabetta, Frediani, Paola, Naranjo, Juan Carlos +1
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.10398

Abstract

We study the local geometry of the moduli space of intermediate Jacobians of (2,2)-threefolds in \mathbb P² × \mathbb P². More precisely, we prove that a composition of the second fundamental form of the Siegel metric in \mathcal A₉ restricted to this moduli space, with a natural multiplication map is a nonzero holomorphic section of a vector bundle. We also describe its kernel. We use the two conic bundle structures of these threefolds, Prym theory, gaussian maps and Jacobian ideals.

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