Related papers: Automorphisms of order three on numerical Godeaux …
We show that a 3-manifold containing an incompressible surface has topologically minimal surfaces of arbitrary high genus.
First we show that any group of automorphisms of null-entropy of a projective hyperk\"ahler manifold $M$ is almost abelian of rank at most $\rho(M) - 2$. We then characterize automorphisms of a K3 surface with null-entropy and those with…
In the present paper we prove that finite symplectic groups of automorphisms of manifolds of k3^[n] type can be obtained by deforming natural morphisms arising from K3 surfaces if and only if they satisfy a certain numerical condition.
A $3$-polytope is a $3$-connected, planar graph. It is called unigraphic if it does not share its vertex degree sequence with any other $3$-polytope, up to graph isomorphism. The classification of unigraphic $3$-polytopes appears to be a…
It is known that the automorphism group of any projective K3 surface is finitely generated [24]. In this paper, we consider a certain kind of K3 surfaces with Picard number 3 whose automorphism groups are isomorphic to congruence subgroups…
It is known that an automorphism group of a K3 surface with Picard number two is either infinite cyclic group or infinite dihedral group if it is infinite. In this paper, we study the generators of an automorphism group. We use the…
We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface arising as the orbit space of such a contracting…
In this article we study compact Riemann surfaces with a non-large group of automorphisms of maximal order; namely, compact Riemann surfaces of genus $g$ with a group of automorphisms of order $4g-4.$ Under the assumption that $g-1$ is…
We present a finite set of generators of the automorphism group of a supersingular K3 surface with Artin invariant 1 in characteristic 3.
Recently there has been renewed interest in the mapping-class group of a compact surface of genus $g \ge 2$ and also in its finite order elements. A finite order element of the mapping-class group will be a conformal automorphisms on some…
We classify isotopy classes of automorphisms (self-homeomorphisms) of 3-manifolds satisfying the Thurston Geometrization Conjecture. The classification is similar to the classification of automorphisms of surfaces developed by Nielsen and…
We will show that there is a smooth complex projective surface, birational to some Enriques surface, such that the automorphism group is discrete but not finitely generated.
This paper shows that the automorphism group of a Beauville surface is a finite solvable group, and describes its possible structure. It relies on results of Singerman on triangle group inclusions, and of Lucchini on generators for special…
We give a simple example of a polynomial contraction automorphism of $\mathbb C^d$, $ d\ge 3 $, with unbounded degree growth. Combined with Poincar\'e-Dulac theorem it provides an algebraic automorphism of $\mathbb C^d$, $ d\ge 3 $, which…
This is a survey of the Kawamata-Morrison cone conjecture on the structure of Calabi-Yau varieties and more generally Calabi-Yau pairs. We discuss the proof of the cone conjecture for algebraic surfaces, with plenty of examples. We show…
Self-rational maps of generic algebraic K3 surfaces are conjectured to be trivial. We relate this conjecture to a conjecture concerning the irreducibility of the universal Severi varieties parametrizing nodal curves of given genus and…
The structure of binary self-dual codes invariant under the action of a cyclic group of order $pq$ for odd primes $p\neq q$ is considered. As an application we prove the nonexistence of an extremal self-dual $[96, 48, 20]$ code with an…
An automorphism of an algebraic surface $S$ is called cohomologically (numerically) trivial if it acts identically on the second $l$-adic cohomology group (this group modulo torsion subgroup). Extending the results of S. Mukai and Y.…
This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…
The purpose of this paper is to complete the classification of binary self-dual [48,24,10] codes with an automorphism of odd prime order. We prove that if there is a self-dual [48, 24, 10] code with an automorphism of type p-(c,f) with p…