منابع مشابه
Tilting Bundles via the Frobenius Morphism
Let X be be a smooth algebraic variety over an algebraically closed field k of characteristic p > 0, and F : X → X the absolute Frobenius morphism. In this paper we develop a technique for computing the cohomology groups H(X, End(F∗OX)) and show that these groups vanish for i > 0 in a number of cases that include some toric Fano varieties, blowups of the projective plane (e.g., Del Pezzo surfac...
متن کاملTheta divisors and the Frobenius morphism
We introduce theta divisors for vector bundles and relate them to the ordinariness of curves in characteristic p > 0. We prove, following M. Raynaud, that the sheaf of locally exact differentials in characteristic p > 0 has a theta divisor, and that the generic curve in (any) genus g ≥ 2 and (any) characteristic p > 0 has a cover that is not ordinary (and which we explicitely construct). 1 Thet...
متن کاملStability of Direct Images under Frobenius Morphism
Let X be a smooth projective variety over an algebraically field k with char(k) = p > 0 and F : X → X1 be the relative Frobenius morphism. When dim(X) = 1, we prove that F∗W is a stable bundle for any stable bundle W (Theorem 2.3). As a step to study the question for higher dimensional X , we generalize the canonical filtration (defined by Joshi-Ramanan-Xia-Yu for curves) to higher dimensional ...
متن کاملFrobenius Splitting for Schubert Varieties
This thesis presents an expository account of the use of Frobenius splitting techniques in the study of Schubert varieties. After developing the basic theory of Frobenius splitting, we show that the Schubert and Bott-Samelson varieties are split and use this to derive geometric consequences in arbitrary characteristic. The main result highlighted is that Schubert varieties are normal, Cohen-Mac...
متن کاملFrobenius Morphism and Semi-stable Bundles
This article is the expanded version of a talk given at the conference: Algebraic geometry in East Asia 2008. In this notes, I intend to give a brief survey of results on the behavior of semi-stable bundles under the Frobenius pullback and direct images. Some results are new.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1995
ISSN: 0021-8693
DOI: 10.1006/jabr.1995.1135