Related papers: Projective Automorphism Groups of Nonsingular Quar…

In this paper, we study a generalization of the notion of AS-regularity for connected $\mathbb{Z}$-algebras. Our main result is a characterization of those categories equivalent to noncommutative projective schemes associated to right…

We classify the automorphism groups of del Pezzo surfaces of degrees one and two over an algebraically closed field of characteristic two. This finishes the classification of automorphism groups of del Pezzo surfaces in all characteristics.

This article initiates a geometric study of the automorphism groups of general graph products of groups, and investigates the algebraic and geometric structure of automorphism groups of cyclic product of groups. For a cyclic product of at…

We present a finite set of generators of the automorphism group of a supersingular K3 surface with Artin invariant 1 in characteristic 3.

The set of all subspaces of a given dimension in a finite classical polar space has a structure of a symmetric association scheme. If the dimension is zero, this is the scheme of the collinearity graph of the space; If the dimension is…

The special linear groups, the mapping class groups of surfaces, the outer autormorphism groups of free groups appear in numerous domains. Their analogies, developped in particular in K. Vogtmann's work, have been written about a lot. In…

We study automorphisms of the Hilbert scheme of $n$ points on a generic projective K3 surface $S$, for any $n \geq 2$. We show that the automorphism group of $S^{[n]}$ is either trivial or generated by a non-symplectic involution and we…

In positive characteristic, algebraic curves can have many more automorphisms than expected from the classical Hurwitz's bound. There even exist algebraic curves of arbitrary high genus g with more than 16g^4 automorphisms. It has been…

A normal subgroup of the (extended) mapping class group of a surface is said to be geometric if its automorphism group is the mapping class group. We prove that in the case of the Cantor tree surface, every normal subgroup is geometric. We…

We show, in this first part, that the maximal number of singular points of a normal quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic $2$ is at most $16$. We produce examples with…

Consider a smooth connected algebraic group $G$ acting on a normal projective variety $X$ with an open dense orbit. We show that Aut($X$) is a linear algebraic group if so is $G$; for an arbitrary $G$, the group of components of Aut($X$) is…

Macbeath gave a formula for the number of fixed points for each non-identity element of a cyclic group of automorphisms of a compact Riemann surface in terms of the universal covering transformation group of the cyclic group. We observe…

Let $S$ be a regular minimal surface of general type over the field of complex numbers, and $\mathrm{Aut}_\mathbb{Q}(S)$ the subgroup of automorphisms acting trivially on $H^*(S,\mathbb{Q})$. It has been known since twenty years that…

Quaternionic Shimura surfaces are quotient of the bidisc by an irreducible cocompact arithmetic group. In the present paper we are interested in (smooth) quaternionic Shimura surfaces admitting an automorphism with one dimensional fixed…

We shall show the existence of 15 automorphic forms of weight 8 on the moduli space of marked Hessian quartic surfaces of cubic surfaces. These automorphic forms can be interpreted in terms of the coefficients of the Sylvester form of a…

We classify the automorphism group of minimal surfaces of general type with $K_S^2 = 1$ and $\rho_g = 2$. Furthermore, we show that the order of the automorphism group is bounded above by 200 and can only have prime factors $p \leq 31$ with…

We classify del Pezzo surfaces with Du Val singularities that have infinite automorphism groups, and describe the connected components of their automorphisms groups.

In this second part we study first the group $Aut_{\mathbb Q}(S)$ of numerically trivial automorphisms of an algebraic properly elliptic surface $S$, that is, of a minimal algebraic surface with Kodaira dimension $\kappa(S)=1$, in the case…

We construct an example of a field and a del Pezzo surface of degree $2$ over this field without points such that its automorphism group is isomorphic to $\mathrm{PSL}_2(\mathbb{F}_7) \times \mathbb{Z}/2\mathbb{Z},$ which is the largest…

In this paper, we prove that each automorphism of a surface braid group is induced by a homeomorphism of the underlying surface, provided that this surface is a closed, connected, orientable surface of genus at least 2, and the number of…