Hermitian-Yang-Mills approach to the conjecture of Griffiths on the positivity of ample vector bundles

It is often true that certain moduli problems of varieties or of vector bundles over a fixed variety have as coarse moduli scheme an integral variety.. In this case

Rendiconti del Seminario Matematico della Università di Padova, tome 89 (1993),

Since the space of positive definite Hermitian forms is a convex set, the existence of a metric in E over a compact space X follows from the existence of partitions

In [36], Siu and Yau proved the Frankel conjecture that every compact K¨ ahler manifold with positive holomorphic bisectional curvature is biholomorphic to the projective space..

In [36], Siu and Yau proved the Frankel conjecture that every compact K¨ ahler manifold with positive holomorphic bisectional curvature is biholomorphic to the projective space..

This gives an example of a positively curved singular Her- mitian metric on a vector bundle with no smooth Griffiths semipositive Hermitian metrics.. If there is a smooth Hermitian

We consider vector bundles, by which we mean torsion free, coherent sheaves on a nonsingular projective variety X.. These

Definition. — A vector bundle E on a scheme X is ample if for every coherent sheaf F, there is an integer UQ>O, such that for every n^-n^, the sheaf FOS^E) (where S^E) is the 71 th