Stability of Arakelov bundles and tensor products without global sections.
In questa nota si danno dei criteri per la stabilità di fasci di quartiche piane.
A monomial self-map on a complex toric variety is said to be -stable if the action induced on the -cohomology is compatible with iteration. We show that under suitable conditions on the eigenvalues of the matrix of exponents of , we can find a toric model with at worst quotient singularities where is -stable. If is replaced by an iterate one can find a -stable model as soon as the dynamical degrees of satisfy . On the other hand, we give examples of monomial maps , where this condition...
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...
A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures that have opposite...
We determine the stable cohomology groups ( of the alternating groups for all integers n and i, and all odd primes p.