On Non-vanishing of Cohomologies of Generalized Raynaud Polarized Surfaces
نویسنده
چکیده
We consider a family of slightly extended version of the Raynaud’s surfaces X over the field of positive characteristic with Mumford-Szpiro type polarizations Z, which have Kodaira non-vanishing H(X,Z) 6= 0. The surfaces are at least normal but smooth under a special condition. We compute the cohomologies H(X,Z) for i, n ∈ Z and study their (non-)vanishing. Finally, we give a fairly large family of non Mumford-Szpiro type polarizations Za,b with Kodaira non-vanishing. MSC classification: (Primary: 14J25, 14J17; secondary: 13D99)
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