Related papers: On the stable dynamical spectrum of complex surfac…

We give a complete classification of finite groups acting symplectically on supersingular K3 surfaces of Artin invariant one. Using work of Dolgachev and Keum, this provides the full classification of tame finite symplectic automorphism…

Given a pair of translation surfaces it is very difficult to determine whether they are supported on the same algebraic curve. In fact, there are very few examples of such pairs. In this note we present infinitely many examples of finite…

We derive explicit equations for the Oguiso-Yu automorphism of minimum topological entropy on a complex Enriques surface. The approach is computer aided and makes use of elliptic fibrations.

We consider translation surfaces with poles on surfaces. We shall prove that any finite group appears as the automorphism group of some translation surface with poles. As a direct consequence we obtain the existence of structures achieving…

In this paper, we consider the automorphisms of fine curve graphs restricted to continuously $k$-differentiable curves. We show that for closed surfaces with genus at least 2, they are induced by homeomorphisms of the surface.

The $i$-th eigenvalue $\lambda_i$ of the Laplace-Beltrami operator on a surface can be considered as a functional on the space of all Riemannian metrics of unit volume on this surface. Surprisingly only few examples of extremal metrics for…

In this paper, we study the Abreu equation on toric surfaces. In particular, we prove the existence of the positive extremal metric when relative $K$-stability is assumed.

We show that, as in de Rham cohomology over the complex numbers, the value of the entropy of an automorphism of the surface over a finite field $\F_q $ is taken on the span of the N\'eron-Severi group inside of $\ell$-adic cohomology. v2:…

We present a notion of a random toric surface modeled on a notion of a random graph. We then study some threshold phenomena related to the smoothness of the resulting surfaces.

We compute entropies in a large family of K3 surface automorphisms in (P^1)^3. In keeping with a result by Xie, we find that the entropies vary in a lower semi-continuous manner as the Picard ranks of the K3 surfaces vary.

Extending the analogous result of Cannon and Wagreich for the fundamental groups of surfaces, we show that, for the l-regular graphs X associated to regular tessellations of hyperbolic plane by m-gons, the denominators of the growth series…

We show that any birational selfmap of a complex projective surface that has dynamical degree greater than one and is defined over a number field automatically satisfies the Bedford-Diller energy condition after a suitable birational…

We compute the number of moduli of all irreducible components of the moduli space of smooth curves on Enriques surfaces. In most cases, the moduli maps to the moduli space of Prym curves are generically injective or dominant. Exceptional…

We describe the topology of singular real algebraic curves in a smooth surface. We enumerate and bound in terms of the degree the number of topological types of singular algebraic curves in the real projective plane.

The present paper provides several results on automorphisms of hyperk\"ahler (or irreducible holomorphic symplectic) manifolds. In particular it focuses on the symplectic case and contains a classification of prime order symplectic…

If a map has k transitivity classes of vertices that are subject to the action of the automorphism group, it is said to be k-uniform. The classification of 1-uniform maps on the torus is known. In this article, we classify 2-uniform maps on…

We give a notion of ordinary Enriques surfaces and their canonical lifts in any positive characteristic, and we prove Torelli-type results for this class of Enriques surfaces.

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…

This is the abstruct of the revised paper. We study the equivariant analytic torsion for K3 surfaces with an anti-symplectic involution with the invariant lattice M (such a surface is called a 2-elementary K3 surface of type M in this…

We give an example of a dominant rational selfmap of the projective plane whose dynamical degree is a transcendental number.