ON THE BMY INEQUALITY ON SURFACES

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2022-2-10

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Terzi, Sadık

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In the thesis, we are concerned with the relation between the ordinarity of surfaces of general type and the failure of the BMY inequality in positive characteristic. We consider semistable fibrations π : S −→ C where S is a smooth projective surface and C is a smooth projective curve. Using the exact sequence relating the locally exact differential forms on S, C, and S/C, we prove an inequality relating c21 and c2 for ordinary surfaces which admit generically ordinary semistable fibrations. This inequality differs from the BMY inequality by a correcting term which vanishes if the fibration is ordinary. In the last chapter we discuss an alternative approach which relates the failure of the Bogomolov inequality (c21 ≤ 4c2) on a surface X to the existence of torsors for some special X-group schemes.

Subject Keywords

BMY inequality, ordinarity, semistable fibrations, torsors

URI

https://hdl.handle.net/11511/96219

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

S. Terzi, “ON THE BMY INEQUALITY ON SURFACES,” Ph.D. - Doctoral Program, Middle East Technical University, 2022.