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On the local geometry of the moduli space of $(2,2)$-threefolds in ${\mathcal A}_9$

Author:
Elisabetta Colombo, Paola Frediani, Juan Carlos Naranjo, Gian Pietro Pirola
Keyword:
Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)
journal:
--
date:
2023-10-15 16:00:00
Abstract
We study the local geometry of the moduli space of intermediate Jacobians of $(2,2)$-threefolds in ${\mathbb P}^2 \times {\mathbb P}^2$. More precisely, we prove that a composition of the second fundamental form of the Siegel metric in $\mathcal A_9$ 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.
PDF: On the local geometry of the moduli space of $(2,2)$-threefolds in ${\mathcal A}_9$.pdf
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