On Frobenius-destabilized Rank-2 Vector Bundles over Curves
نویسنده
چکیده
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 bundle F∗L is stable. (2) The rational map V has base points, i.e., there exist stable bundles E over X1 such that F ∗E is not semistable. (3) If g = 2, p > 2 and X ordinary, the number of base points of V is at most 2 3 p(p − 1).
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