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...
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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...
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We investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.
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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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 ...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1997
ISSN: 0040-8735
DOI: 10.2748/tmj/1178225109