Stability of the tangent bundle and existence of a Kähler-Einstein metric.
In this paper nondegenerate multidimensional matrices of boundary format in V0 ⊗ ... ⊗ Vp are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix A the stabilizer for the SL(V0) x ... x SL(Vp)-action, Stab(A), is completely described. In particular we prove that there exists an explicit action of SL(2) on V0 ⊗ ... ⊗ Vp such that Stab(A)0 ⊆ SL(2) and the equality holds if and only if A belongs to a unique SL(V0) x ... x SL(Vp)-orbit...
We present a novel approach for bounding the resolvent of for large energies. It is shown here that there exist a large integer and a large number so that relative to the usual weighted -norm, for all . This requires suitable decay and smoothness conditions on . The estimate (2) is trivial when , but difficult for large since the gradient term exactly cancels the natural decay of the free resolvent. To obtain (2), we introduce a conical decomposition of the resolvent and then sum over...
For any smooth projective variety, we study a birational invariant, defined by Campana which depends on the Kodaira dimension of the subsheaves of the cotangent bundle of the variety and its exterior powers. We provide new bounds for a related invariant in any dimension and in particular we show that it is equal to the Kodaira dimension of the variety, in dimension up to 4, if this is not negative.