Ricerc@Sapienza

The aim of this research project is to investigate the positivity of certain families of differential forms arising from Griffiths positive hermitian holomorphic vector bundles.
On the cohomology classes level the issue has been completely solved by Fulton and Lazarsfeld, who showed that the positive polynomials in the Chern classes of an ample vector bundle are exactly those belonging to the positive convex cone spanned by the Schur polynomials in the Chern classes of the bundle.
More generally, for differential forms the question remains open in both directions.
Partial answers are due to the works of Guler and Diverio, which show that Segre forms (namely, special Schur polynomials in the Chern forms) are positive for Griffiths positive vector bundles.
Motivated by these results, this research aims to investigate which differential forms in the positive convex cone spanned by the Schur polynomials in the Chern forms are positive for Griffiths positive vector bundles.