论文标题
$ \ operatorname {pgl} _4的所有有限原始组的不变平滑四分之一表面（\ mathbb {c}）$
Invariant Smooth Quartic Surfaces by all Finite Primitive Groups of $\operatorname{PGL}_4(\mathbb{C})$
论文作者
论文摘要
对于每个有限的原始子组$ g $ of $ \ operatatorName {pgl} _4（\ mathbb {c}）$，我们找到了所有平滑的$ g $ g $ invariant Quartic Quartic表面。我们还在$ \ permatatorName中找到所有忠实表示形式{pgl} _4（\ mathbb {c}）$的平滑四分之一$ g $ g $ -Invariant表面：$ \ mathfrak {a} a} _5，_5，\ mathfrak { \ operatorName {psl_2（\ Mathbb {f} _7）}，\ Mathfrak {a} _6，\ Mathbb {z} _2^4 \ rtimes \ rtimes \ rtimes \ mathbb {z} _5 $ and $ \ m artbb {z} _} _2^4 \ rtime dimme dimme dimme。这些组的原始表示完全是$ \ operatorName {pgl} _4（\ mathbb {c}）$的子组，$ \ mathbb {p}^3 $不是$ g $ -susuper arion。作为副产品，我们表明，具有最大的投射自动形态的光滑四分之一表面由$ \ {x_0^4 + x_1^4 + x_1^4 + x_2^4 + x_3^4 + x_3^4 + 12 x_1 x_1 x_1 x_2 x_2 x_3 = 0 \} $（唯一到projective equivalence）。
For each finite primitive subgroup $G$ of $\operatorname{PGL}_4(\mathbb{C})$, we find all the smooth $G$-invariant quartic surfaces. We also find all the faithful representations in $\operatorname{PGL}_4(\mathbb{C})$ of the smooth quartic $G$-invariant surfaces by the groups: $\mathfrak{A}_5,\mathfrak{S}_5, \operatorname{PSL_2(\mathbb{F}_7)},\mathfrak{A}_6,\mathbb{Z}_2^4\rtimes\mathbb{Z}_5$ and $\mathbb{Z}_2^4\rtimes D_{10}$. The primitive representation of these groups are precisely the subgroups of $\operatorname{PGL}_4(\mathbb{C})$ for which $\mathbb{P}^3$ is not $G$-super rigid. As a byproduct, we show that the smooth quartic surface with the biggest group of projective automorphism is given by $\{ x_0^4 + x_1^4 + x_2^4 + x_3^4 + 12 x_0 x_1 x_2 x_3= 0\}$ (unique up to projective equivalence).
