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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.
In many cases rational surfaces obtained by desingularization of birational dynamical systems are not relatively minimal. We propose a method to obtain coordinates of relatively minimal rational surfaces by using blowing down structure. We apply this
In this paper, following Grothendieck {it Esquisse dun programme}, which was motivated by Belyis work, we study some properties of surfaces $X$ which are triangulated by (possibly ideal) isometric equilateral triangles of one of the spherical, euclid
We will show that any open Riemann surface $M$ of finite genus is biholomorphic to an open set of a compact Riemann surface. Moreover, we will introduce a quotient space of forms in $M$ that determines if $M$ has finite genus and also the minimal genus where $M$ can be holomorphically embedded.
It was known to von Neumann in the 1950s that the integer lattice $mathbb{Z}^2$ forms a uniqueness set for the Bargmann-Fock space. It was later demonstrated by Seip and Wallsten that a sequence of points $Gamma$ that is uniformly close to the intege
Let $X$ be a hyperbolic curve over a field $k$ finitely generated over $mathbb{Q}$. A Galois section $s$ of $pi_{1}(X)tomathrm{Gal}(bar{k}/k)$ is birational if it lifts to a section of $mathrm{Gal}(overline{k(X)}/k(X))tomathrm{Gal}(bar{k}/k)$. Grothe