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

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

moduli space is known to carry the natural structure of a Hausdorff complex analytic space [L-O, Nor], or of a quasiprojective algebraic scheme when M is algebraic [Gie,

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

We exhibit a transformation taking special Lagrangian submanifolds of a Calabi-Yau together with local systems to vector bundles over the mirror manifold with connections

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

Finally we define what it means for h to be strictly negatively curved in the sense of Nakano and show that it is possible to regularise such metrics with a sequence of smooth,