Effective Non-vanishing for Algebraic Surfaces in Positive Characteristic I
نویسنده
چکیده
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.
منابع مشابه
Effective 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 کاملOn Non-vanishing of Cohomologies of Generalized Raynaud Polarized Surfaces
We consider a family of slightly extended version of the Raynaud’s surfaces X over the field of positive characteristic with Mumford-Szpiro type polarizations Z, which have Kodaira non-vanishing H(X,Z) 6= 0. The surfaces are at least normal but smooth under a special condition. We compute the cohomologies H(X,Z) for i, n ∈ Z and study their (non-)vanishing. Finally, we give a fairly large famil...
متن کاملRims-1736 Counterexamples of Kodaira’s Vanishing and Yau’s Inequality in Positive Characteristics
We generalize Tango’s theorem [T1] on the Frobenius map of the first cohomology groups to higher dimensional algebraic varieties in characteristic p > 0. As application we construct counterexamples of Kodaira vanishing in higher dimension, and prove the Ramanujam type vanishing on a surface which is not of general type when p ≥ 5. Let X be a smooth complete algebraic variety over an algebraical...
متن کاملm / 9 60 40 12 v 1 1 9 A pr 1 99 6 ELEMENTARY COUNTEREXAMPLES TO KODAIRA VANISHING IN PRIME CHARACTERISTIC
Using methods from the modular representation theory of algebraic groups one can construct [1] a projective homogeneous space for SL 4 in prime characteristic , which violates Kodaira vanishing. In this note we show how elementary algebraic geometry can be used to simplify and generalize this example. Let X be a smooth projective variety of dimension m over an algebraically closed field of char...
متن کاملThere Exist Nontrivial Threefolds with Vanishing Hodge Cohomology
We analyse the structure of the algebraic manifolds Y of dimension 3 with H(Y,ΩjY ) = 0 for all j ≥ 0, i > 0 and h 0(Y,OY ) > 1, by showing the deformation invariant of some open surfaces. Secondly, we show when a smooth threefold with nonconstant regular functions satisfies the vanishing Hodge cohomology. As an application of these theorems, we give the first example of non-affine, non-product...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005