Algebraic curves admitting non-collinear Galois points

Algebraic curves with collinear Galois points

A criterion for the existence of a birational embedding into a projective plane with three collinear Galois points for algebraic curves is presented. The extendability of an automorphism induced by a Galois point to a linear transformation of the projective plane is also discussed, under the assumption that two Galois points exist.

Algebraic curves admitting inner and outer Galois points

There are two purposes in this article. One is to present a criterion for the existence of a birational embedding into a projective plane with inner and outer Galois points for algebraic curves. Another is to classify plane curves of degree $d$ admitting an inner Galois point $P$ and an outer Galois point $Q$ with $G_PG_Q=G_P \rtimes G_Q$ or $G_P \ltimes G_Q$, under the assumption that the characteristic $p$ is zero or $p$ does not divide $d-1$.

具有两个Galois点的代数曲线的后代

Descendants of algebraic curves admitting two Galois points

本文研究代数曲线的Galois点与商曲线的联系，引入具有两个Galois点的后代概念，并证明Fermat曲线的后代均为Fermat曲线，其次数为素数时无后代。

Algebraic curves admitting the same Galois closure for two projections

A criterion for the existence of a plane model of an algebraic curve such that the Galois closures of projections from two points are the same is presented. As an application, it is proved that the Hermitian curve in positive characteristic coincides with the Galois closures of projections of some plane curve from some two non-uniform points.

允许极化伽罗瓦自同态的簇

Varieties Admitting Polarized Galois Endomorphisms

本文证明了允许内放大伽罗瓦自同态的光滑复射影簇的极大有理连通纤维化为环面纤维化，从而推出有理连通时该簇为环面簇，皮卡德数一时为射影空间，并验证了对数 Calabi-Yau 型猜想。

involution对Hermitian曲线商曲线的Galois线

Galois lines for the quotient curve of the Hermitian curve by an involution

研究involution作用下Hermitian曲线商曲线在有限域上的Galois线排列，确定三种平面模型的Galois点。