Motivic Tubular Neighborhoods

穿孔管状邻域与无穷远处的稳定同伦

Punctured tubular neighborhoods and stable homotopy at infinity

本文增加了∞-范畴余极限综述、穿孔管状邻域显式模型框架及定向类新理论，重新表述主定理并展示如何生成通过基域Grothendieck-Witt环上Smith形式计算的二次Mumford矩阵。

On metrics with minimal singularities of line bundles whose stable base loci admit holomorphic tubular neighborhoods

We investigate the minimal singularities of metrics on a big line bundle $L$ over a projective manifold when the stable base locus $Y$ of $L$ is a submanifold of codimension $r\geq 1$. Under some assumptions on the normal bundle and a neighborhood of $Y$, we give a explicit description of the minimal singularity of metrics on $L$. We apply this result to study a higher (co-)dimensional analogue of Zariski's example, in which the line bundle $L$ is not semi-ample, however it is nef and big.

局部模型的管状邻域

Tubular neighborhoods of local models

本文证明了 $p$-进 shtuka 模空间的 v-sheaf 局部模型是单分支的，确立了 $p \leq 3$ 时 Scholze-Weinstein 猜想的剩余情形，简化了凝聚猜想的证明，并将 Huber 的邻近闭链比较定理推广至 v-sheaf 框架。

Segre-Veronese流形的到达性

Reach of Segre-Veronese Manifolds

本文计算了与单位球面相交的Segre-Veronese簇的到达性、极值曲率及管状邻域体积，揭示了其几何性质。