相关论文: Autour d'une surface rationnelle dans $\mathbb{C}^…

We prove that, for an Enriques surface in odd characteristic, the automorphism group is finitely generated and it acts on the effective nef cone with a rational polyhedral fundamental domain. We also construct a smooth projective surface in…

A cyclic $n$-gonal surface is a compact Riemann surface $X$ of genus $g\geq 2$ admitting a cyclic group of conformal automorphisms $C$ of order $n$ such that the quotient space $X/C$ has genus 0. In this paper, we provide an overview of…

Any compact surface supports a continuous action of the orientation preserving affine group of the real line which is fixed point free (Lima and Plante). It is generally admitted that this action can be taken smooth although it is not easy…

A smooth rational surface X is a Coble surface if the anti-canonical linear system is empty while the anti-bicanonical linear system is non-empty. In this note we shall classify these X and consider the finiteness problem of the number of…

Given a nondegenerate ternary form $f=f(x_1,x_2,x_3)$ of degree 4 over an algebraically closed field of characteristic zero, we use the geometry of K3 surfaces and van den Bergh's correspondence between representations of the generalized…

We survey some recent results on biconservative surfaces in $3$-dimensional space forms $N^3(c)$ with a special emphasis on the $c=0$ and $c=1$ cases. We study the local and global properties of such surfaces, from extrinsic and intrinsic…

Let p be a prime integer, and q a power of p. The Ballico-Hefez curve is a non-reflexive nodal rational plane curve of degree q+1 in characteristic p. We investigate its automorphism group and defining equation. We also prove that the…

Following an approach of Dolgachev, Pinkham and Demazure, we classified in math.AG/0210153 normal affine surfaces with hyperbolic $\C^{*}$-actions in terms of pairs of $\Q$-divisors $(D_+,D_-)$ on a smooth affine curve. In the present paper…

Let $\G$ be a group of type rotating automorphisms of an affine building $\cB$ of type $\wt A_2$. If $\G$ acts freely on the vertices of $\cB$ with finitely many orbits, and if $\Omega$ is the (maximal) boundary of $\cB$, then…

We show that the generic fiber of a family of smooth $\mathbb{A}^{1}$-ruled affine surfaces always carries an $\mathbb{A}^{1}$-fibration, possibly after a finite extension of the base. In the particular case where the general fibers of the…

We prove a structure theorem for non-isomorphic endomorphisms of weak Q-Fano threefolds, or more generally for threefolds with big anti-canonical divisor. Also provided is a criterion for a fibred rationally connected threefold to be…

This is a survey of the geometry of complex cubic fourfolds with a view toward rationality questions. Topics include classical constructions of rational examples, Hodge structures and special cubic fourfolds, associated K3 surfaces and…

We provide the first known example of a finite group action on an oriented surface $T$ that is free, orientation-preserving, and does not extend to an arbitrary (in particular, possibly non-free) orientation-preserving action on any compact…

We show by finding an explicit parametrization that a 4th degree surface which arises as a necessary condition for the existence of a perfect cuboid is a rational surface, i.e. birationally equivalent over $\mathbb Q$ to a plane.

Define $QC(n)$ to be the number of quasiplatonic topological actions of the cyclic group $C_n$ on surfaces of genus at least two. We use formulas of Benim and Wootton to give an explicit formula for $QC(n)$. In addition, we relate the…

Let F be a finite field of characteristic p. We consider smooth surfaces over F(t) defined by an equation f+tg=0, where f and g are forms of degree d in 4 variables with coefficients in F, with d prime to p. We prove : For such surfaces…

Kummer surfaces are special quartic surfaces that admit $16$ nodes. The automorphisms of K3 Kummer surfaces are rich and complicated. Based on the results of Keum and Kond\=o, and as a continuation of the recent result by He and Yang, we…

Let $G$ be a finite 2-group and $K$ be a field satisfying that (i) $\fn{char}K\ne 2$, and (ii) $\sqrt{a}\in K$ for any $a\in K$. If $G$ acts on the rational function field $K(x,y,z)$ by monomial $K$-automorphisms, then the fixed field…

Conformal/anticonformal actions of the quasi-abelian group $QA_{n}$ of order $2^n$, for $n\geq 4$, on closed Riemann surfaces, pseudo-real Riemann surfaces and closed Klein surfaces are considered. We obtain several consequences, such as…

In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real…