Derived-tame algebras and non-commutative nodal projective curves

这个项目的目标是发展一个类似于Geigle和Lenzing的加权射影直线理论的非对易节点射影曲线的系统理论。特别地，我们想要澄清这样一条曲线上的凝聚层的派生范畴何时允许倾斜对象，并描述以这种方式产生的倾斜代数类。我们特别感兴趣的是当我们开始的非对易节点曲线(结果是相应的倾斜代数)具有驯服的派生表示类型的情况。利用这种方法，我们期望用新的方法来处理关于球面对象的旧问题和射影直线循环上的派生相干层范畴的自等价。

The goal of this project is to develop a systematic theory of non-commutative nodal projective curves, similar to the theory of weighted projective lines of Geigle and Lenzing. In particular, we want to clarify when the derived category of coherent sheaves on such a curve admits a tilting object, and describe the classes of tilted algebras arising in this way. We are especially interested in the case when the non-commutative nodal curve we start with (and as a result, the corresponding tilted algebra) has tame derived representation type.Using this approach, we anticipate to treat with new methods old problems about spherical objects and auto-equivalences of the derived category of coherent sheaves on a cycle of projective lines.