We shall give, in an optimal form, a sufficient numerical condition for the finiteness of the fundamental group of the smooth locus of a normal K3 surface. We shall moreover prove that, if the normal K3 surface is elliptic and the above fundamental group is not finite, then there is a finite covering which is a complex torus.

Based on a novel application of an archimedean type pairing to the geometry and deformation theory of K3 surfaces, we construct a regulator indecomposable K1-class on a self-product of a K3 surface. In the Appendix, we explain how this pairing is a special instance of a general pairing on precycles in the equivalence relation defining Bloch’s higher Chow groups.

We compute the three-graviton tree amplitude in Type IIB superstring theory compact-ified to six dimensions using the manifestly (6d) supersymmetric Berkovits-Vafa-Witten worldsheet variables. We consider two cases of background geometry: the flat space example R 6 × K3, and the curved example AdS 3 × S 3 × K3 with Ramond flux, and compute the correlation functions in the bulk.

Using Hassett’s isomorphism between the Noether-Lefschetz moduli space C26 of special cubic fourfolds X ⊂ P of discriminant 26 and the moduli space F14 of polarized K3 surfaces of genus 14, we use the family of 3-nodal scrolls of degree seven in X to show that the universal K3 surface over F14 is rational.

In this paper we give a characterization of the height of K3 surfaces in characteristic p > 0. This enables us to calculate the cycle classes of the loci in families of K3 surfaces where the height is at least h. The formulas for such loci can be seen as generalizations of the famous formula of Deuring for the number of supersingular elliptic curves in characteristic p. In order to describe the...

Integrated steady state rate equations have been used to determine the kinetic constants (Vs, Ks, Vp, and Kp) and rate constants (k1, k2, k3, and k4) of the reversible enzyme mechanism: (see article). The fumarase reaction has been used as a model to illustrate the procedures for determining these constants. In contrast to initial velocity studies, the values of the constants have been obtained...

Using a quaternionic formulation of the moduli space M (IIA/K3) of 10D type IIA superstring on a generic K3 complex surface with volume V 0, we study extremal N = 2 black attractors in 6D space-time and their uplifting to 7D. For the 6D theory, we exhibit the role played by 6D N = 1 hypermultiplets and the Zm central charges isotriplet of the 6D N = 2 superalgebra. We construct explicitly the s...

INTRODUCTION To determine the differentiation of human limbal epithelial cells in tissue culture. MATERIALS AND METHODS Epithelial cells from the human limbus (n = 29) were isolated and cultured in supplemental hormonal epithelial medium (SHEM) in the presence of mitomycin C-treated 3T3 feeder layer. Confluent cells were airlifted to form multiple layers. The expression of cytokeratin 3 (K3),...

Let S be a smooth minimal K3 surface defined over C , G a finite group acting on S. The induced linear action of G on H 0 (ω S) ∼ = C leads to an exact sequence 1 −→ K −→ G −→ N −→ 1 , where the non-symplectic part N is a cyclic group Z m , which acts on the intermediate quotient S/K which is also K3. It is well-known that the Euler number ϕ(m) of m must divide 22 − ρ(S) ([N], Corollary 3.3), i...

this experiment was conducted to determin the effect of 25(h)d3 and k3 vitamins on immune system of ross 308 broiler chicken in a completely randomized design with a 3×4 factorial arrangement with four replicates and 16 observation per replicate. treatments included vitamine d3 (0, 0.4, 0.6 and 0.8 μg) and vitamin k3 (0, 2 and 6 μg). on day 180 g incubation 0.5 ml of treatment solution was inju...