Differential forms and quadrics of the canonical image

Abstract

We extend some of the results of [PZ] and we prove a criterion for a family π : X → B of n-dimensional varieties of general type and with Albanese morphism of degree 1 to have birational fibers. We do not assume that the canonical map of the general fiber is a morphism nor that the canonical linear system has no fixed components. We also prove some instances of the generic Torelli theorem under the assumption, natural in this context, that the fibers are minimal and their minimal model is unique. It is trivial to construct counterexamples to generic Torelli without such minimality assumptions.

On Massey products and Rational homogeneous varieties

“…The theory of adjoint forms was introduced in [CP] and [PZ] and later developed and applied in [Ra], [PR], [CNP], [G-A], [BGN], [RZ1], and recently [CRZ]. The basic idea is to study global 1-forms and n-forms of a complex smooth variety of dimension n to get some information on its infinitesimal deformations.…”

Fujita decomposition and Massey product for fibered varieties

“…, η n on the fiber F b and build their adjoint form in the usual way, which we briefly recall. For an extensive discussion on the topic, we refer to [RZ1].…”

“…In [PT] this study is done for a fibred surface f : S → B; we generalise and extend the results of [PT]. We recall that Massey products have been introduced in [CP] and [PZ] and then applied in [Ra], [PR], [CNP], [G-A], [BGN], [RZ1], [RZ2], [RZ3] and recently [CRZ]. The basic construction is as follows.…”

Fujita Decomposition and Massey Product for Fibered Varieties

“…In [15], the relation between the rank of U , the genus, and the Clifford index of the general fiber is studied. We recall that Massey products have been introduced in [10], [26] and then applied in [1], [9], [14], [24], [28], [30]- [32] and recently in [8], [29]. The basic construction is as follows.…”