带表观奇点的算子（oper）的分层与等单值泡裂（isomonodromic bubbling）
Stratification of opers with apparent singularities and isomonodromic bubbling
AI总结：
在亏格≥2的紧黎曼曲面上，研究Simpson的秩2平坦联络de Rham模空间分层，构造表观奇点碰撞消失的全纯族，关联等单值泡裂手术，实现分层闭包关系。
摘要：
在亏格g≥2的紧黎曼曲面上，我们研究Simpson提出的秩2平坦联络的de Rham模空间的分层。通过将平坦SL₂(ℂ)联络表示为分支射影结构，或等价地表示为带表观奇点的算子（oper），包含某平坦联络的分层由表示该联络所需的最少表观奇点数量决定。我们构造了显式全纯族，其中两个简单表观奇点碰撞并消失，使该族进入更小的分层；这实现了Simpson关于一般点附近分层的闭包关系。希格斯丛的类似族由谱曲线上的Baker–Akhiezer除子描述，其中两个点收敛到被谱对合交换的一对点。我们证明，碰撞前，两个表观奇点由界定一个泡的双路径连接，因此这些族源于Calsamiglia、Deroin和Francaviglia讨论的等单值泡裂（isomonodromic bubbling）手术。
英文摘要：
On a compact Riemann surface of genus $g \geq 2$, we study Simpson's stratification of the de Rham moduli space of rank-2 flat connections. Upon representing flat $\mathrm{SL}_2(\mathbb{C})$-connections by branched projective structures, or equivalently by opers with apparent singularities, the stratum containing a flat connection is determined by the minimal number of apparent singularities needed to represent it. We construct explicit holomorphic families in which two simple apparent singularities collide and disappear, so that the family crosses into a smaller stratum; this realizes Simpson's closure relation between strata near generic points. The analogous families of Higgs bundles are described by Baker--Akhiezer divisors on the spectral curve in which two points converge to a pair of points exchanged by the spectral involution. We show that, before the collision, the two apparent singularities are joined by twin paths bounding a bubble, so that these families arise from the isomonodromic bubbling surgery discussed by Calsamiglia, Deroin and Francaviglia.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
