Counterexamples of the Kawamata-Viehweg Vanishing on Ruled Surfaces in Positive Characteristic
نویسنده
چکیده
We give a classification of the counterexamples of the Kawamata-Viehweg vanishing on a geometrically ruled surface in terms of the Tango invariant of the base curve.
منابع مشابه
Counterexamples to the Kawamata-Viehweg Vanishing on Ruled Surfaces in Positive Characteristic
We give counterexamples to the Kawamata-Viehweg vanishing theorem on ruled surfaces in positive characteristic, and prove that if there is a counterexample to the Kawamata-Viehweg vanishing theorem on a geometrically ruled surface f : X → C, then either C is a Tango curve or all of sections of f are ample.
متن کاملEffective Non-vanishing for Algebraic Surfaces in Positive Characteristic
We give a partial answer to the effective non-vanishing problem for algebraic surfaces in positive characteristic, and also give counterexamples for the Kawamata-Viehweg vanishing and the logarithmic semipositivity on ruled surfaces in positive characteristic.
متن کاملEffective Non-vanishing for Algebraic Surfaces in Positive Characteristic I
We give a partial answer to the effective non-vanishing problem for algebraic surfaces in positive characteristic, and also give counterexamples for the Kawamata-Viehweg vanishing and the logarithmic semipositivity on ruled surfaces in positive characteristic.
متن کاملKawamata-Viehweg Vanishing on Rational Surfaces in Positive Characteristic
We prove that the Kawamata-Viehweg vanishing theorem holds on rational surfaces in positive characteristic by means of the lifting property to W2(k) of certain log pairs on smooth rational surfaces. As a corollary, the Kawamata-Viehweg vanishing theorem holds on log del Pezzo surfaces in positive characteristic.
متن کاملSe p 20 09 Strongly Liftable Schemes and the Kawamata - Viehweg Vanishing in Positive Characteristic ∗
A smooth schemeX over a field k of positive characteristic is said to be strongly liftable, if X and all prime divisors on X can be lifted simultaneously over W2(k). In this paper, we give some concrete examples and properties of strongly liftable schemes. As an application, we prove that the Kawamata-Viehweg vanishing theorem in positive characteristic holds on any normal projective surface wh...
متن کامل