## FILIPPO FAGIOLI

PhD Graduate**PhD program:**: XXXIV

**supervisor**: D. Fiorenza

**advisor**: S. Diverio

**Thesis title:**Positivity of characteristic forms via pointwise universal push-forward formulae

Given a Hermitian holomorphic vector bundle over a complex manifold, consider its flag bundles with the associated universal vector bundles endowed with the induced metrics. We show that the universal formula for the push-forward of a homogeneous polynomial in the Chern classes of the universal vector bundles also holds pointwise at the level of Chern forms in this Hermitianized situation.
As an application, we obtain the positivity of several polynomials in the Chern forms of Griffiths semipositive vector bundles not previously known.
This gives new evidences towards a conjecture proposed by Griffiths, which has raised interest in the past as well as in recent years. This conjecture can be interpreted as a pointwise Hermitianized version of the Fulton--Lazarsfeld theorem on numerically positive polynomials for ample vector bundles.

**Research products**

11573/1677586 - 2022 -

**Pointwise universal Gysin formulae and applications towards Griffiths' conjecture**Diverio, Simone; Fagioli, Filippo - 01a Articolo in rivista

**paper:**ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE (Pisa: Scuola Normale Superiore) pp. 1597-1624 - issn: 2036-2145 - wos: WOS:000906589400001 (1) - scopus: (0)

11573/1619551 - 2022 -

**A note on Griffiths' conjecture about the positivity of Chern–Weil forms**Fagioli, F. - 01a Articolo in rivista

**paper:**DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS (Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: nlinfo-f@elsevier.nl, INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598) pp. 1-15 - issn: 0926-2245 - wos: WOS:000788835500003 (2) - scopus: 2-s2.0-85123881834 (1)