Transitivity on Weierstrass points

Weierstrass points of superelliptic curves

In this lecture we give a brief introduction to Weierstrass points of curves and computational aspects of $q$-Weierstrass points on superelliptic curves.

On Sokhotski--Casorati--Weierstrass theorem on metric spaces

In a neighborhood of isolated point of a domain of a metric space, a behavior of generalized quasiconformal mappings is studied. It is proved that, mappings mentioned above have continuous extension to the domain at some additional conditions. As consequence, an analog of Sokhotski--Weierstrass theorem is obtained.

局部完全交与Weierstrass点

Local Complete Intersections and Weierstrass Points

本文证明了在局部完全交条件下，具有对称Weierstrass半群的完全积分Gorenstein曲线的模空间是加权射影空间，且适用于正特征域。

On nonnegatively graded Weierstrass points

We provide a new lower bound for the dimension of the moduli space of smooth pointed curves with prescribed Weierstrass semigroup at the marked point, derived from the Deligne-Greuel formula and Pinkham's equivariant deformation theory. Using Buchweitz's description of the first cohomology module of the cotangent complex for monomial curves, we show that our lower bound improves a recently one given by Pflueger. By allowing semigroups running over suitable families of symmetric semigroups of multiplicity six, we show that this new lower bound is attained, and that the corresponding moduli spac…

An Oka Principle for a Parametric Infinite Transitivity Property

It is an elementary fact that the action by holomorphic automorphisms on C^n is infinitely transitive, i.e., m-transitive for any m in N. The same holds on any Stein manifold with the holomorphic density property X. We study a parametrized case: we consider m points on X parametrized by a Stein manifold W, and seek a family of automorphisms of X, parametrized by W, putting them into a standard form which does not depend on the parameter. This general transitivity is shown to enjoy an Oka principle, to the effect that the obstruction to a holomorphic solution is of a purely topological nature. …

关于紧黎曼曲面上仅在单点有极点的亚纯函数的注记

A note on meromorphic functions on a compact Riemann surface having poles at a single point

本文基于黎曼-罗赫定理，利用上同调群维数证明紧黎曼曲面上单点极点亚纯函数的魏尔斯特拉斯间隙定理，发现相关组合问题并给出魏尔斯特拉斯点的注记及推论。