Derived categories, quasi-hereditary algebras, and toric geometry (A08)

派生范畴及其变换在几何、代数和表示理论中起着核心作用。本文主要研究箭图表示的射影代数簇和模空间上倾斜丛的存在和构造。有时导出的等价关系涉及附加信息，如t-结构、对偶、例外序列、正交分解或某些子范畴。在许多情况下，出现了最高权范畴和准遗传代数。

Derived categories and their transformations play a central role in geometry, algebra and representation theory. In this project we focus on the existence and construction of tilting bundles on projective algebraic varieties and moduli spaces of quiver representations. Sometimes derived equivalences respect additional information like t-structures, dualities, exceptional sequences, orthogonal decompositions or certain subcategories. In many cases highest weight categories and quasi-hereditary algebras show up.