Parallelisms and Translations of (Affine) SL(2,q)-Unitals

Automorphisms of (Affine) SL(2,q)-Unitals

$\operatorname{SL}(2,q)$-unitals are unitals of order $q$ admitting a regular action of $\operatorname{SL}(2,q)$ on the complement of some block. They can be obtained from affine $\operatorname{SL}(2,q)$-unitals via parallelisms. We compute a sharp upper bound for automorphism groups of affine $\operatorname{SL}(2,q)$-unitals and show that exactly two parallelisms are fixed by all automorphisms. In $\operatorname{SL}(2,q)$-unitals obtained as closures of affine $\operatorname{SL}(2,q)$-unitals via those two parallelisms, we show that there is one block fixed under the full automorphism group.

Three Affine SL(2,8)-Unitals

$\operatorname{SL}(2,q)$-unitals are unitals of order $q$ admitting a regular action of $\operatorname{SL}(2,q)$ on the complement of some block. We introduce three non-classical affine $\operatorname{SL}(2,8)$-unitals and their full automorphism groups. Each of those three affine unitals can be completed to at least two non-isomorphic unitals, leading to six pairwise non-isomorphic unitals of order $8$.

Veronese空间理论中的超平面、平行性及相关问题

Hyperplanes, parallelisms, and related problems in the theory of Veronese Spaces

我们研究Veronese空间与仿射空间的平行性，确定Veronese空间与射影空间的超平面，并分析这些超平面所确定的平行性的几何。

部分仿射空间和反演空间的完成结果

A Completion Result for Partial Affine and Inversive Spaces

本文改进了有限仿射平面的完成界限，并研究了更高维设计和反演空间的完成问题。