Moduli of vector bundles on curves in positive characteristics

被引：12
|
作者：
Joshi, K [1 ]
Xia, EZ [1 ]
机构：
[1] Univ Arizona, Dept Math, Tucson, AZ 85721 USA
来源：
COMPOSITIO MATHEMATICA | 2000年 / 122卷 / 03期
关键词：
algebraic curves; Frobenius morphism; moduli schemes; vector bundles;
D O I：
10.1023/A:1001864401294
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli scheme of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 (with determinant equal to a theta characteristic) whose Frobenius pull-back is not semi-stable. The indeterminacy of the Frobenius map at this point can be resolved by introducing Higgs bundles.
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收藏
页码：315 / 321
页数：7
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