Dynamics with small entropy on projective K3 surfaces

Automorphisms of projective K3 surfaces with minimum entropy

Surfaces via Almost - Primes

Based on the result on derived categories on K3 surfaces due to Mukai and Orlov and the result concerning almost-prime numbers due to Iwaniec, we remark the following facts: (1) For any given positive integer N , there are N (mutually non-isomorphic) projective complex K3 surfaces such that their Picard groups are not isomorphic but their transcendental lattices are Hodge isometric, or equivale...

Projective Models of K3 Surfaces with an Even Set

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a careful analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate the...

N ov 2 00 6 PROJECTIVE MODELS OF K 3 SURFACES WITH AN EVEN SET

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a carefull analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate th...

Groups of Automorphisms of Null-entropy of Hyperkähler Manifolds

The following two results are proven: The full automorphism group of any non-projective hyperkähler manifold M is almost abelian of rank at most maximum of ρ(M) − 1 and 1. Any groups of automorphisms of nullentropy of a projective hyperkähler manifold M is almost abelian of rank at most ρ(M) − 2. A few applications for K3 surfaces are also given.