Log canonical thresholds of Del Pezzo Surfaces in characteristic p

Details Log canonical thresholds of Del Pezzo Surfaces in characteristic p Log canonical thresholds of Del Pezzo Surfaces in characteristic p

2012-03-05

arxiv.org/abs/1203.0995v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

The log canonical threshold for all smooth complex Del Pezzo surfaces was computed by Cheltsov. His proof used connectivity and adjunction-type results, relying on vanishing theorems not known to be true in characteristic p. We compute the log canonical threshold of nonsingular Del Pezzos over an arbitrary algebraically closed field. We give an algebraic proof of this adjunction for surfaces and avoid the use of connectivity by classifying curves of small degree. This can be applied to show that in characteristic p Del Pezzos of small degree are K-semistable.

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