18 research outputs found
Strong Stability of Cotangent Bundles of Cyclic Covers
Let be a smooth projective variety over an algebraically closed field
of characteristic of and Picard number .
Suppose that satisfies H^i(X,F^{m*}_X(\Omg^j_X)\otimes\Ls^{-1})=0 for any
ample line bundle \Ls on , and any nonnegative integers with
, where is the absolute Frobenius
morphism. We prove that by procedures combining taking smooth hypersurfaces of
dimension and cyclic covers along smooth divisors, if the resulting
smooth projective variety has ample (resp. nef) canonical bundle
, then \Omg_Y is strongly stable resp. strongly semistable
with respect to any polarization.Comment: To appear in Comptes Rendus Math\'ematiqu
-Dolbeault resolution of the lowest Hodge piece of a Hodge module
Let be a complex space and a pure Hodge module with strict support
. The purpose of this paper is to introduce a coherent subsheaf
of M. Saito's which is a combination of and the
multiplier ideal sheaf while constructing a resolution
of by differential forms with certain -boundary conditions.
This could be viewed as a wide generalization of MacPherson's conjecture on the
-representation of the Grauert-Riemenschneider sheaf. As applications,
various vanishing theorems for (Saito's vanishing, Kawamata-Viehweg
vanishing and some new ones like Nadel vanishing, partial vanishing) are proved
via standard differential geometrical arguments.Comment: 25 pages. Comments are welcome