论文标题
kodaira循环的球形物体，传递性和自动等值通过温和的代数
Spherical objects, transitivity and auto-equivalences of Kodaira cycles via gentle algebras
论文作者
论文摘要
本文研究了投影线的任何kodaira $ n $ cycle上的球形对象类，并根据$ n $ undust的圆环在没有自行体上的封闭式曲线上提供了其同构类别的参数化。在柔和的代数上采用了最新的结果，我们为任何Kodaira循环的有限派生类别提供了拓扑模型。计算这些类别的三角自动等量组的组，并显示出对球形对象的同构类别的运输作用。这回答了波兰奇克的一个问题，并扩展了Burban-Kreussler和Lekili-Polishchuk的早期结果。对自动等量的描述进一步用于建立Sibilla定义的映射类群体行动的忠诚。最后一部分描述了对应于向量束和简单向量束的封闭曲线。这导致了Bodnarchuk-Drozd-Greuel结果的替代证明，该证明指出，射影线周期上的简单向量捆绑在其多度，等级和决定符中独特地确定。作为副产品，我们获得了Burban-Drozd-Greuel介绍的$ C_N $上任何简单矢量捆绑包的循环序列的封闭公式。
This paper studies the class of spherical objects over any Kodaira $n$-cycle of projective lines and provides a parametrization of their isomorphism classes in terms of closed curves on the $n$-punctured torus without self-intersections. Employing recent results on gentle algebras, we derive a topological model for the bounded derived category of any Kodaira cycle. The groups of triangle auto-equivalences of these categories are computed and are shown to act transitively on isomorphism classes of spherical objects. This answers a question by Polishchuk and extends earlier results by Burban-Kreussler and Lekili-Polishchuk. The description of auto-equivalences is further used to establish faithfulness of a mapping class group action defined by Sibilla. The final part describes the closed curves which correspond to vector bundles and simple vector bundles. This leads to an alternative proof of a result by Bodnarchuk-Drozd-Greuel which states that simple vector bundles on cycles of projective lines are uniquely determined by their multi-degree, rank and determinant. As a by-product we obtain a closed formula for the cyclic sequence of any simple vector bundle on $C_n$ as introduced by Burban-Drozd-Greuel.
