Abstract
AbstractWe study deformations of rational curves and their singularities in positive characteristic. We use this to prove that if a smooth and proper surface in positive characteristicpis dominated by a family of rational curves such that one member has all δ-invariants (resp. Jacobian numbers) strictly less than12(p-1){\frac{1}{2}(p-1)}(resp.p), then the surface has negative Kodaira dimension. We also prove similar, but weaker results hold for higher-dimensional varieties. Moreover, we show by example that our result is in some sense optimal. On our way, we obtain a sufficient criterion in terms of Jacobian numbers for the normalization of a curve over an imperfect field to be smooth.
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Schedule a callMore From: Journal für die reine und angewandte Mathematik (Crelles Journal)
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