平面曲线奇点的单值性与箭图突变
Monodromy of plane curve singularities and quiver mutation
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中文总结 AI 辅助
该研究证明可形变实Morsification的箭图突变类唯一确定平面曲线奇点的整单值性模，建立了Fomin等人猜想在可分不可约情形下的代数到拓扑蕴含关系。
中文摘要 AI 辅助
本文的主要结果表明，可形变实Morsification的箭图突变类唯一确定平面曲线奇点的整单值性模。特别地，我们证明可分划分的箭图突变类唯一确定不可约平面曲线奇点的复拓扑类型，这在可分不可约情形下建立了S. Fomin、P. Pylyavskyy、E. Shustin与D. Thurston猜想中代数到拓扑的蕴含关系。该结果通过在微分双分次Ginzburg代数上连续有限维dg模的导出范畴中基于等变欧拉配对发展表示论技术得以证明，关键步骤是利用这些技术证明plabic fence的箭图突变类唯一恢复相关光滑链环Alexander模的挠部分。
英文摘要
The main result of this article shows that the quiver mutation class of a malleable real Morsification uniquely determines the integral monodromy module of a plane curve singularity. In particular, we show that the quiver mutation class of a malleable divide determines the complex topological type of an irreducible plane curve singularity. This establishes the algebraic-to-topological implication of a conjecture of S.~Fomin, P.~Pylyavskyy, E.~Shustin and D.~Thurston in the malleable irreducible case. The result is proven by developing representation-theoretic techniques based on an equivariant Euler pairing in the derived category of continuous finite-dimensional dg modules over a differential bigraded Ginzburg algebra. A key step uses these techniques to show that the quiver mutation class of a plabic fence uniquely recovers the torsion part of the Alexander module of the associated smooth link.
