Generating the plane Cremona groups by involutions

Abstract

We prove that over any perfect field the plane Cremona group is generated by involutions.

Figures (31)

• Figure 1: Sarkisov links between rational surfaces over a perfect field
• Figure 2: The birational map $\varepsilon\colon\mathbb{P}^2\dashrightarrow\mathbb{P}^1\times\mathbb{P}^1$ from Lemma \ref{['lem:GeometricDescriptionOfExorcist']}.
• Figure 3: The two pieces of Lemma \ref{['lem:linkD5']}\ref{['item:linkD5--fibering']}
• Figure 4: Sarkisov links between rational surfaces over $\mathbf R$
• Figure B.1: $\mathcal{P}(\mathbb{P}^2;1,1)$, $\mathcal{P}(\mathbb{F}_0;1)$

Theorems & Definitions (139)

• Theorem 1.1
• Corollary 1.2
• Lemma 2.1
• proof
• Proposition 2.2
• Proposition 2.3
• Theorem 2.4
• Proposition 2.5
• proof
• Remark 2.6