In this thesis we study in details the theory of adjoint forms which was introduced by Collino and Pirola in the case of smooth curves and then generalized in higher dimension by Pirola and Zucconi. Useful generalizations are given, for example for Gorenstein curves, smooth projective hypersurfaces and fibrations over a smooth curve. The main applications of this theory concern infinitesimal Torelli problems and criteria which ensure that a family $\mathcal{X}\to B$ of algebraic varieties of general type and with Albanese morphism of degree $1$ has birational fibers.

Adjoint forms and algebraic families / Luca Rizzi - Udine : . , 2017 Apr 03. ((29. ciclo

### Adjoint forms and algebraic families

#### Abstract

In this thesis we study in details the theory of adjoint forms which was introduced by Collino and Pirola in the case of smooth curves and then generalized in higher dimension by Pirola and Zucconi. Useful generalizations are given, for example for Gorenstein curves, smooth projective hypersurfaces and fibrations over a smooth curve. The main applications of this theory concern infinitesimal Torelli problems and criteria which ensure that a family $\mathcal{X}\to B$ of algebraic varieties of general type and with Albanese morphism of degree $1$ has birational fibers.
##### Scheda breve Scheda completa Scheda completa (DC)
Adjoint forms; Infinitesimal Torelli problem; Extension class of a vector bundle
Adjoint forms and algebraic families / Luca Rizzi - Udine : . , 2017 Apr 03. ((29. ciclo
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/1132961