559 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
China’s Emerging Inter-network Society - The Rise of Public Advocacy in the Digital ‘Public Sphere’
Ph.D
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