Abstract
Let X be a smooth projective variety over an algebraically closed field k of characteristic p>0 of dimX≥4 and Picard number ρ(X)=1. Suppose that X satisfies Hi(X,FXm⁎(ΩXj)⊗L−1)=0 for any ample line bundle L on X, and any nonnegative integers m,i,j with 0≤i+j<dimX, where FX:X→X is the absolute Frobenius morphism. Let Y be a smooth variety obtained from X by taking hyperplane sections of dim ≥3 and cyclic covers along smooth divisors. If the canonical bundle ωY is ample (resp. nef), then we prove that ΩY is strongly stable (resp. strongly semistable) with respect to any polarization.
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