On vector bundles destabilized by Frobenius pull-back
نویسندگان
چکیده
منابع مشابه
On vector bundles destabilized by Frobenius pull-back
Let X be a smooth projective curve of genus g > 1 over an algebraically closed field of positive characteristic. This paper is a study of a natural stratification, defined by the absolute Frobenius morphism of X, on the moduli space of vector bundles. In characteristic two, there is a complete classification of semi-stable bundles of rank 2 which are destabilized by Frobenius pull-back. We also...
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Let X be a smooth projective curve of genus g ≥ 2 over an algebraically closed field k of characteristic p > 0. Let MX be the moduli space of semistable rank-2 vector bundles over X with trivial determinant. The relative Frobenius map F : X → X1 induces by pull-back a rational map V : MX1 99K MX . In this paper we show the following results. (1) For any line bundle L over X , the rank-p vector ...
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Let X be a smooth projective curve of genus g ≥ 2 defined over an algebraically closed field k of characteristic p > 0. For p sufficiently large (explicitly given in terms of r, g) we construct an atlas for the locus of all Frobenius-destabilized bundles (i.e. we construct all Frobenius-destabilized bundles of degree zero up to isomorphism). This is done by exhibiting a surjective morphism from...
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We give a class of examples of a vector bundle on a relative smooth projective curve over SpecZ such that for infinitely many prime reductions the bundle has a Frobenius descent, but the generic restriction in characteristic zero is not semistable. Mathematical Subject Classification (2000): primary: 14H60, secondary: 13A35.
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Let C be a smooth curve, and Mr(C) the coarse moduli space of vector bundles of rank r and trivial determinant on C. We discuss the generalized Verschiebung map Vr : Mr(C) 99K Mr(C) induced by pulling back under Frobenius. We begin with a survey of general background results on the Verschiebung, as well as certain more specialized work in fixed genus, characteristic, and rank. We then discuss t...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2006
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x05001788