ShengYuan Zhao | Searcharxiv

arXiv2021

Centralizers of elements of infinite order in plane Cremona groups

Let $\mathbf{K}$ be an algebraically closed field. The Cremona group $\operatorname{Cr}_2(\mathbf{K})$ is the group of birational transformations of the projective plane $\mathbb{P}^2_{\mathbf{K}}$. We carry out an overall study of centralizers of elements of infinite order in $\operatorname{Cr}_2(\mathbf{K})$ which leads to a classification of embeddings of $\mathbf{Z}^2$ into $\operatorname{Cr}_2(\mathbf{K})$, as well as a classification of maximal non-torsion abelian subgroups of $\operatorname{Cr}_2(\mathbf{K})$ when $\operatorname{char}(\mathbf{K})=0$.

math.AG↗

arXiv2021

Uniqueness of birational structures on Inoue surfaces

We prove that the natural $(\operatorname{Aff} _2(\mathbf{C}),\mathbf{C}^2)$-structure on an Inoue surface is the unique $(\operatorname{Bir}(\mathbb{P}^2),\mathbb{P}^2(\mathbf{C}))$-structure, generalizing a result of Bruno Klingler which asserts that the natural $(\operatorname{Aff}_2(\mathbf{C}),\mathbf{C}^2)$-structure is the unique $(\operatorname{PGL} _3(\mathbf{C}),\mathbb{P}^2(\mathbf{C}))$-structure.

math.CV↗