论文标题
关于等级两个稳定捆的注释
A note on rank two stable bundles over surfaces
论文作者
论文摘要
令$π：x \ longrightArrow c $是纤维上的纤维，在曲线$ c $上降低了纤维，并考虑在cubly $ x $上的偏光$ h $。让$ e $是$ c $上的稳定矢量套件$ 2 $。我们证明，回调$π^*e $是$ x $上的$ h-$ stable捆绑包。该结果使我们能够将稳定捆绑包的相应模量空间$ \ MATHCAL {M} _C（2，D）$和$ \ MATHCAL {M} _ {X，H}（2，DF，0）$通过Injective Morphism通过。我们研究了Brill-Noether基因座水平上的诱导型态度，以在纤维表面上构建Brill-Noether基因座的示例。关于Brill-Noether基因座空虚的结果是由于Clifford定理对表面上的两个捆绑包的概括。
Let $π: X \longrightarrow C$ be a fibration with reduced fibers over a curve $C$ and consider a polarization $H$ on the surface $X$. Let $E$ be a stable vector bundle of rank $2$ on $C$. We prove that the pullback $π^*E$ is a $H-$stable bundle over $X$. This result allows us to relate the corresponding moduli spaces of stable bundles $\mathcal{M}_C(2,d)$ and $\mathcal{M}_{X,H}(2,df,0)$ through an injective morphism. We study the induced morphism at the level of Brill-Noether loci to construct examples of Brill-Noether loci on fibered surfaces. Results concerning the emptiness of Brill-Noether loci follow as a consequence of a generalization of Clifford's Theorem for rank two bundles on surfaces.
