论文标题
飞机cremona组的发电机在田野上有两个要素
Generators of the plane Cremona group over the field with two elements
论文作者
论文摘要
在有限场上$ \ mathbb {f} _2 $上的飞机cremona组是由三个无限家庭生成的，有限的许多基本轨道的birational Maps。一个家庭通过一个点保留了线铅笔，另外两个家庭通过四个点保留了圆锥形的铅笔，形成一个尺寸为4的galois轨道或两个尺寸2的galois轨道。对于每个家庭，我们给出了一个由$ \ mathbb {f} _2 _2 $的生成集。此外，我们描述了有限的剩余地图，并在生成Cremona组所需的数字上给出了上限。最后，我们证明了$ \ mathbb {f} _2 $的平面cremona组是通过互动生成的。
The plane Cremona group over the finite field $\mathbb{F}_2$ is generated by three infinite families and finitely many birational maps with small base orbits. One family preserves the pencil of lines through a point, the other two preserve the pencil of conics through four points that form either one Galois orbit of size 4, or two Galois orbits of size 2. For each family, we give a generating set that is parametrized by the rational functions over $\mathbb{F}_2$. Moreover, we describe the finitely many remaining maps and give an upper bound on the number needed to generate the Cremona group. Finally, we prove that the plane Cremona group over $\mathbb{F}_2$ is generated by involutions.
