We extend the theory of Pirola and Zucconi (J Algebraic Geom 12(3):535–572, 2003). We introduce the new notion of adjoint quadric for canonical images of irregular varieties. Using this new notion, we obtain the infinitesimal Torelli theorem for varieties whose canonical image is a complete intersection of hypersurfaces of degree > 2 and for Schoen surfaces. Finally, we show that a family with fiberwise liftable holomorphic forms such that the fibers have Albanese morphism of degree 1 is birationally trivial if there exist no adjoint quadrics.

Differential forms and quadrics of the canonical image

Zucconi F.
2020

Abstract

We extend the theory of Pirola and Zucconi (J Algebraic Geom 12(3):535–572, 2003). We introduce the new notion of adjoint quadric for canonical images of irregular varieties. Using this new notion, we obtain the infinitesimal Torelli theorem for varieties whose canonical image is a complete intersection of hypersurfaces of degree > 2 and for Schoen surfaces. Finally, we show that a family with fiberwise liftable holomorphic forms such that the fibers have Albanese morphism of degree 1 is birationally trivial if there exist no adjoint quadrics.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/1181542
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