Projective Models of K3 Surfaces with an Even Set

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...

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...

Severi varieties and self rational maps of K3 surfaces

0.1 Notations. We deal in this paper with complex projective K3 surfaces, i.e. smooth K-trivial complex projective surfaces without irregularity. Let φ : S 99K S be a dominant self rational map. Suppose Pic(S) = Z. Then there exists a positive integer l such that φOS(1) ∼= OS(l). It is the algebraic degree of φ, that is the degree of the polynomials defining φ. There always exists an eliminatio...

Dynamics with small entropy on projective K3 surfaces

Supersingular K3 Surfaces in Characteristic 2 as Double Covers of a Projective Plane

For every supersingular K3 surface X in characteristic 2, there exists a homogeneous polynomial G of degree 6 such that X is birational to the purely inseparable double cover of P defined by w = G. We present an algorithm to calculate from G a set of generators of the numerical Néron-Severi lattice of X. As an application, we investigate the stratification defined by the Artin invariant on a mo...