On characteristic forms of positive vector bundles, mixed discriminants and pushforward identities

Siarhei Finski (1)

1 IF - Institut Fourier

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.

Mots clés: Chern classes; Positive vector bundles; Mixed discriminants; Schur polynomials

Domaines: Géométrie différentielle [math.DG]; Géométrie algébrique [math.AG]; Algèbres d'opérateurs [math.OA]

Siarhei Finski. On characteristic forms of positive vector bundles, mixed discriminants and pushforward identities. 2020. ⟨hal-02943833v1⟩