发表机构
École Polytechnique Fédérale de Lausanne; Yonsei University（洛桑联邦理工学院; 延世大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究曲线的上同调Hall代数对Quot概形同调的作用，引入虚拟同调，证明挠CoHA与shuffle代数及Yang-Baxter算子相关，并用于确定tautological关系及新基，最后给出加倍构造。
AI 中文摘要
我们研究曲线的上同调Hall代数及其在Quot概形同调上的作用。我们引入Quot概形的虚拟同调，并证明其在创生与湮灭作用下均保持不变。我们证明挠CoHA同构于一个shuffle代数，且等价地同构于与Yang-Baxter算子相关联的braided对称代数。我们利用这一描述确定了punctual Quot概形的tautological关系理想，并为其上同调环获得了一个新基。最后，我们引入了一种普适的方法来加倍挠CoHA，并证明它自然地作用于任意类型Quot概形的虚拟同调上。
英文摘要
We study cohomological Hall algebras of curves and their actions on the homology of Quot schemes. We introduce the virtual homology of Quot schemes and show that it is preserved by both creation and annihilation actions. We prove that the torsion CoHA is isomorphic to a shuffle algebra and, equivalently, to a braided symmetric algebra associated with a Yang-Baxter operator. We use this description to determine the ideal of tautological relations for punctual Quot schemes and obtain a new basis for their cohomology rings. Finally, we introduce a universal way to double the torsion CoHA and show that it acts naturally on the virtual homology of Quot schemes of arbitrary type.
CommentsComments are welcome. 60 pages
