Simone Diverio (SAPIENZA Università di Roma)
Title: Pointwise universal Gysin formulae and positivity of some characteristic forms
Abstract:
In the last few years there has been a renewed interest around an old conjecture by Griffiths
characterizing which should be the positive characteristic forms for any given Griffiths positive
holomorphic Hermitian vector bundle. According to this conjecture, they should be precisely the
characteristic forms belonging to the positive cone spanned by the Schur forms. After recalling
the various notions of positivity for holomorphic Hermitian vector bundles, and how they are
(or should be) related, we shall explain a recent result obtained in collaboration with my
PhD student F. Fagioli, which gives a partial confirmation of the above conjecture. Such a result
is obtained as a consequence of a pointwise, differential-geometric Gysin formula for the push-forward
of the curvature of the tautological line bundles over flag bundles.