论文标题
温和代数的淤泥理论的几何实现
A geometric realization of silting theory for gentle algebras
论文作者
论文摘要
温和的代数产生了对多边形的定向标记表面的解剖，而温和代数的有界派生类别在该表面上具有几何解释。在本文中，我们根据其基础表面研究了温和代数的有界衍生类别的淤积理论。特别是，我们展示了淤积突变是如何与分级弧的变化相对应的，并且在某些情况下，淤积突变会导致八面体公管的解释，而在四边形在四边形中的对角线的翻转，例如在dyckerhoff-kapranov的工作中，在变形的表面上。我们还表明，减少淤积的比对应于切割基础表面，就像沼泽 - 帕鲁（Marsh-Palu）和Qiu-Zhou所示的Calabi-yau降低表面群集类别一样。
A gentle algebra gives rise to a dissection of an oriented marked surface with boundary into polygons and the bounded derived category of the gentle algebra has a geometric interpretation in terms of this surface. In this paper we study silting theory in the bounded derived category of a gentle algebra in terms of its underlying surface. In particular, we show how silting mutation corresponds to the changing of graded arcs and that in some cases silting mutation results in the interpretation of the octahedral axioms in terms of the flipping of diagonals in a quadrilateral as in the work of Dyckerhoff-Kapranov in the context of triangulated surfaces. We also show that silting reduction corresponds to the cutting of the underlying surface as is the case for Calabi-Yau reduction of surface cluster categories as shown by Marsh-Palu and Qiu-Zhou.
