We study the local geometry of the moduli space of intermediate Jacobians of (2,2)-threefolds in P^2x P^2. More precisely, we prove that a composition of the second fundamental form of the Siegel metric in 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.
On the local geometry of the moduli space of (2,)-threefolds in A_9
Paola Frediani;Juan Carlos Naranjo;Gian Pietro Pirola
In corso di stampa
Abstract
We study the local geometry of the moduli space of intermediate Jacobians of (2,2)-threefolds in P^2x P^2. More precisely, we prove that a composition of the second fundamental form of the Siegel metric in 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.File in questo prodotto:
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