AI 中文总结
本文针对亏格g≥4的曲线，在秩2情形下构造反例，证明de Rham模空间算子分层的叶状结构猜想不成立，原因是相邻分层间全纯曲线处切平面不连续。
AI 中文摘要
设X为亏格g的光滑复射影曲线，𝒯_dR(X,r)为秩r的平丛模空间。在稳定轨迹上，Simpson证明了具有拉格朗日纤维的算子分层，并提出这些纤维是否闭合且能组合成光滑叶状结构的问题，该问题常被称为叶状结构猜想。本文在每条亏格g≥4的曲线上，给出了秩2时该猜想的反例，核心思路是证明沿穿越两个相邻分层的全纯曲线，切平面不连续，因此叶状结构断言不成立。
英文摘要
Let $X$ be a smooth complex projective curve of genus $g$, and let $\mathcal{M}_{\mathrm{dR}}(X,r)$ be the moduli space of flat bundles of rank $r$. Over the stable locus, Simpson showed the oper stratification with Lagrangian fibers and asked whether these fibers are closed and fit together into a smooth foliation. This question is often referred to as the foliation conjecture. In this paper, we give a counterexample to this conjecture in rank two on every curve of genus $g\geq4$. The main idea is to show that the tangent planes are discontinuous along a holomorphic curve crossing two adjacent strata, hence the foliation assertion fails.
Comments11 pages, comments are welcome!
