On characteristic forms of positive vector bundles, mixed discriminants and pushforward identities
Résumé
We prove that Schur polynomials in Chern forms of Nakano and dual Nakano positive vector bundles are positive as differential forms. Moreover, modulo a statement about the positivity of a "double mixed discriminant" of linear operators on matrices, which preserve the cone of positive-definite matrices, we establish that Schur polynomials in Chern forms of Griffiths-positive vector bundles are weakly-positive as differential forms.
An important step in our proof is to establish a certain pushforward identity for characteristic forms, refining the determinantal formula of Kempf-Laksov for homolorphic vector bundles on the level of differential forms. In the same vein, we establish a local version of Jacobi-Trudi identity.
Origine : Fichiers produits par l'(les) auteur(s)
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