کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4665416 | 1633814 | 2015 | 37 صفحه PDF | دانلود رایگان |
Let X be a smooth projective curve of genus g≥2g≥2 defined over an algebraically closed field k of characteristic p>0p>0. For p>r(r−1)(r−2)(g−1)p>r(r−1)(r−2)(g−1) we construct an atlas for the locus of all Frobenius-destabilized bundles of rank r (i.e. we construct all Frobenius-destabilized bundles of rank r and degree zero up to isomorphism). This is done by exhibiting a surjective morphism from a certain Quot-scheme onto the locus of stable Frobenius-destabilized bundles. Further we show that there is a bijective correspondence between the set of stable vector bundles E over X such that the pull-back F⁎(E)F⁎(E) under the Frobenius morphism of X has maximal Harder–Narasimhan polygon and the set of opers having zero p-curvature. We also show that, after fixing the determinant, these sets are finite, which enables us to derive the dimension of certain Quot-schemes and certain loci of stable Frobenius-destabilized vector bundles over X. The finiteness is proved by studying the properties of the Hitchin–Mochizuki morphism; an alternative approach to finiteness has been realized in [3]. In particular we prove a generalization of a result of Mochizuki to higher ranks.
Journal: Advances in Mathematics - Volume 274, 9 April 2015, Pages 39–75