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

We prove that Schur polynomials in Chern forms of Nakano and dual positive vector bundles are as differential forms. Moreover, modulo a statement about the positivity “double mixed discriminant” linear operators on matrices, which preserve cone definite we establish Griffiths weakly This provides differential-geometric versions Fulton–Lazarsfeld inequalities for ample bundles. An interpretation conditions through operator theory lies core our approach. Another important step proof is to certain pushforward identity characteristic forms, refining determinantal formula Kempf–Laksov holomorphic level In same vein, local version Jacobi–Trudi identity. Then study inverse problem show already over complex surfaces, one cannot characterize (and even ampleness) polynomials, if takes into consideration all quotients bundle.