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

• Elisabetta Colombo ^[1] ; Paola Frediani ^[2] ; Juan Carlos Naranjo ^[3] ; Gian Pietro Pirola ^[2]
  1. [1] University of Milan

     University of Milan

     Milán, Italia

     
  2. [2] University of Pavia

     University of Pavia

     Pavía, Italia

     
  3. [3] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     

  Mostrar afiliaciones +
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 41, Nº 3, 2025, págs. 953-968
• Idioma: inglés
• DOI: 10.4171/RMI/1542
• Enlaces
  • Texto completo
• Resumen

  • We study the local geometry of the moduli space of intermediate Jacobians of (2,2)-threefolds in P2×P2. 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