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arXiv · 1203.0995

Log canonical thresholds of Del Pezzo Surfaces in characteristic p

Jesus Martinez-Garcia
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Abstract

The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Kollár-Shokurov's connectedness principle and other results relying on vanishing theorems of Kodaira type, not known to be true in finite characteristic. We compute the global log canonical threshold of non-singular del Pezzo surfaces over an algebraically closed field. We give algebraic proofs of results previously known only in characteristic $0$. Instead of using of the connectedness principle we introduce a new technique based on a classification of curves of low degree. As an application we conclude that non-singular del Pezzo surfaces in finite characteristic of degree lower or equal than $4$ are K-semistable.

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Jesus Martinez-Garcia. 2014-02-10. Log canonical thresholds of Del Pezzo Surfaces in characteristic p. https://doi.org/10.1007/s00229-014-0668-8

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