论文标题
小属曲线上的等级2束的多重代数
Multiplicity algebras for rank 2 bundles on curves of small genus
论文作者
论文摘要
Hausel引入了一个交换代数 - 多样性代数 - 与HIGGS束模量空间的C^* - 动作的固定点相关联。在这里，我们描述了该代数的固定点，该固定点由非常稳定的等级2矢量束和零HIGGS字段，用于低属曲线。从几何学上讲，代数的关系是由四肢族的家族描述的，我们专注于这个家族的判别，为稳定捆绑包的模量空间提供了新的观点。我们示例中的判别性表明，随着束的变化，我们获得了代数的同构类别的连续变化。
Hausel introduced a commutative algebra -- the multiplicity algebra -- associated to a fixed point of the C^*-action on the Higgs bundle moduli space. Here we describe this algebra for a fixed point consisting of a very stable rank 2 vector bundle and zero Higgs field for a curve of low genus. Geometrically, the relations in the algebra are described by a family of quadrics and we focus on the discriminant of this family, providing a new viewpoint on the moduli space of stable bundles. The discriminant in our examples demonstrates that as the bundle varies, we obtain a continuous variation in the isomorphism class of the algebra.
