Related papers: Automorphisms of order three on numerical Godeaux …

We compute the automorphisms groups of all numerical Godeaux surfaces, i.e. minimal smooth surfaces of general type with K^2 = 1 and p_g = 0, with torsion of the Picard group of order \nu equals 3, 4, or 5. We present explicit…

We classify K3 surfaces with a non-symplectic finite automorphism of high order. It is shown that such an automorphism cannot be of order 60, and for each of the orders 38, 44, 48, 50, 54 and 66, there exists a unique K3 surface with such…

In this paper we provide a complete classification of non-symplectic automorphisms of order nine of complex K3 surfaces.

In this paper we investigate when the generic member of a family of K3 surfaces admitting a non--symplectic automorphism of finite order admits also a symplectic automorphism of the same order. We give a complete answer to this question if…

This paper concerns K3 surfaces with automorphisms of order 11 in arbitrary characteristic. Specifically we study the wild case and prove that a general such surface in characteristic 11 has Picard number 2. We also construct K3 surfaces…

Minimal algebraic surfaces of general type with the smallest possible invariants have geometric genus zero and K^2=1 and are usually called "numerical Godeaux surfaces". Although they have been studied by several authors, their complete…

We give a necessary and sufficient condition for $k$-step nilmanifolds associated with graphs $(k \geq 3)$ to admit Anosov automorphisms. We also prove nonexistence of Anosov automorphisms on certain classes of 2-step and 3-step…

In this paper we present a classification of non-symplectic automorphisms of K3 surfaces whose order is a multiple of seven by describing the topological type of their fixed locus. In the case of purely non-symplectic automorphisms, we…

Automorphisms of handlebodies arise naturally in the a classification of automorphisms of three-manifolds. Among automorphisms of handlebodies, there are certain automorphisms called irreducible (or generic), which are analogues of…

We determine all posible orders of automorphisms of finite order of complex K3 surfaces or of K3 surfaces in characteristic $p>3$. E.g., a positive integer $N$ is the order of an automorphism of a complex K3 surface if and only if…

In this note we present the classification of non-symplectic automorphisms of prime order on K3 surfaces, i.e.we describe the topological structure of their fixed locus and determine the invariant lattice in cohomology. We provide new…

In the present paper we describe the K3 surfaces admitting order 11 automorphisms and apply this to classify log Enriques surfaces of global index 11.

In this paper, we prove that, over an algebraically closed field whose characteristic is not 2,3 nor 7, a pair of a K3 surface and a purely non-symplectic automorphism of order 21 or 42 is unique up to isomorphism.

We give a short proof that every supersingular K3 surface (except possibly in characteristic $2$ with Artin invariant $\sigma=10$) has an automorphism of Salem degree 22. In particular an infinite subgroup of the automorphism group does not…

The aim of this paper is to show the rigidity of homologically trivial actions of prime order on K3 surfaces. To be precise, we show that homotopy K3 surfaces do not admit a periodic diffeomorphism of odd prime order 3 acting trivially on…

We prove that there is a smooth quartic K3 surface automorphism that is not derived from the Cremona transformation of the ambient three-dimensional projective space. This gives a negative answer to a question of Professor Marat Giz.atullin

We prove that a very general projective K3 surface does not admit a dominant self rational map of degree at least two.

Let S be a K3 surface that admits a non-symplectic automorphism $\rho$ of order 3. We divide $S\times \mathbb{P}^1$ by $\rho\times\psi$ where $\psi$ is an automorphism of order 3 of $\mathbb{P}^1$. There exists a threefold ramified cover of…

A non-classical Godeaux surface is a minimal surface of general type with $\chi=K^2=1$ but with $h^{01}\neq0$. We prove that such surfaces fulfill $h^{01}=1$ and they can exist only over fields of positive characteristic at most 5. Like…

In this paper we study K3 surfaces with a non-symplectic automorphism of order 3. In particular, we classify the topological structure of the fixed locus of such automorphisms and we show that it determines the action on cohomology. This…