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… (More)
A geometric model for segmentation of images with missing boundaries is presented. Some classical problems of boundary completion in cognitive images, like the pop up of subjective contours in the famous triangle of Kanizsa, are faced from a surface evolution point of view. The method is based on the mean curvature evolution of a graph with respect to the… (More)
In this paper we study K3 surfaces with a non-symplectic auto-morphism 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 allows us to describe the structure of the moduli space and to show that it has three irreducible components.
The quotient singularities of dimensions two and three obtained from poly-hedral groups and the corresponding binary polyhedral groups admit natural resolutions of singularities as Hilbert schemes of regular orbits whose exceptional fibres over the origin reveal similar properties. We construct a morphism between these two resolutions , contracting exactly… (More)
In this note we present the classification of non-symplectic au-tomorphisms of prime order on K3 surfaces, i.e. we describe the topological structure of their fixed locus and determine the invariant lattice in cohomol-ogy. We provide new results for automorphisms of order 5 and 7 and alternative proofs for higher orders. Moreover, for any prime p, we… (More)
We prove that the mirror symmetry of Berglund-Hübsch-Chiodo-Ruan, applied to K3 surfaces with a non-symplectic involution, coincides with the lattice mirror symmetry.
We present a measurement of the time-dependent CP-violating (CPV) asymmetries in B0-->K(0)(S)pi(0) decays based on 124x10(6) Upsilon(4S)-->BB decays collected with the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC. In a sample containing 122+/-16 signal decays, we obtain the magnitudes of the direct CPV asymmetry… (More)
We study the maps induced on cohomology by a Nikulin (i.e. a symplectic) in-volution on a K3 surface. We parametrize the eleven dimensional irreducible components of the moduli space of algebraic K3 surfaces with a Nikulin involution and we give examples of the general K3 surface in various components. We conclude with some remarks on Morrison-Nikulin… (More)
We study algebraic K3 surfaces (defined over the complex number field) with a symplectic automorphism of prime order. In particular we consider the action of the automorphism on the second cohomology with integer coefficients (by a result of Nikulin this action is independent on the choice of the K3 surface). With the help of elliptic fibrations we… (More)
Nikulin has classified all finite abelian groups acting symplectically on a K3 surface and he has shown that the induced action on the K3 lattice U 3 ⊕ E 8 (−1) 2 depends only on the group but not on the K3 surface. For all the groups in the list of Nikulin we compute the invariant sublattice and its orthogonal complement by using some special elliptic K3… (More)