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摘要翻译：
设C是亏格G>1的光滑射影曲线，Clifford指数为C(C)，设L是C上由其整体截面生成的线丛。态射I:C-->P(H^0(L))=P是很好定义的，I*T是射影空间P的切丛T对C的限制。通过对一个定理的拟然化，我们证明了如果deg L>2G-C(C)-1，则I*T是半稳定的，并说明了它何时也是稳定的。然后证明了2g-c(C)-1次线丛L在多条曲线上的存在性，使得I*T不是半稳定的。最后，我们完全刻划了当C为超椭圆时I*T的（半）稳定性。
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英文标题：
《About the stability of the tangent bundle restricted to a curve》
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作者：
Chiara Camere
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Let C be a smooth projective curve with genus g>1 and Clifford index c(C) and let L be a line bundle on C generated by its global sections. The morphism i:C -->P(H^0(L))=P is well-defined and i*T is the restriction to C of the tangent bundle T of the projective space P. Sharpening a theorem by Paranjape, we show that if deg L>2g-c(C)-1 then i*T is semi-stable, specifying when it is also stable. We then prove the existence on many curves of a line bundle L of degree 2g-c(C)-1 such that i*T is not semi-stable. Finally, we completely characterize the (semi-)stability of i*T when C is hyperelliptic.
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PDF链接：
https://arxiv.org/pdf/0712.0770
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