论文标题
模块的方案在柔和的代数和表面的层压板上
Schemes of modules over gentle algebras and laminations of surfaces
论文作者
论文摘要
我们研究模块的仿射方案在柔和的代数上。我们描述了这些方案的平滑点，我们还详细分析了它们不可还原的组件。我们的几个结果概括了以前已知的结果，例如通过掉落超循环，并结合带模块。一类特殊的温和代数是雅各布式代数，该代数是由未施加的标记表面的三角形产生的。对于这些，我们获得了一组一般tau的装饰不可还原的成分与表面层压板的一组。作为一种应用，我们得到上层群集代数的一组手镯函数（由musiker-schiffler-williams定义）与表面相关的代数与一组通用的caldero-chapoton函数一致。
We study the affine schemes of modules over gentle algebras. We describe the smooth points of these schemes, and we also analyze their irreducible components in detail. Several of our results generalize formerly known results, e.g. by dropping acyclicity, and by incorporating band modules. A special class of gentle algebras are Jacobian algebras arising from triangulations of unpunctured marked surfaces. For these we obtain a bijection between the set of generically tau-reduced decorated irreducible components and the set of laminations of the surface. As an application, we get that the set of bangle functions (defined by Musiker-Schiffler-Williams) in the upper cluster algebra associated with the surface coincides with the set of generic Caldero-Chapoton functions.
