We determine all complex K3 surfaces with Picard rank 20 over Q. Here the NéronSeveri group has rank 20 and is generated by divisors which are defined over Q. Our proof uses modularity, the Artin-Tate conjecture and class group theory. With different techniques, the result has been established by Elkies to show that Mordell-Weil rank 18 over Q is impossible for an elliptic K3 surface. We also a...

dr ≤ K2. C3 φn,θ(u,β) is differentiable with respect to θ and β, and for |φn,θ(u,β)|, |dφn,θ(u,β)/dβ| and |dφn,θ(u,β)/dθ|, the supremum over u ∈ R ,β ∈ b(β,K3), θ ∈ b(θ ,K3) is bounded for some K3 > 0, where b(x, r) denotes the ball centred at x with radius r > 0. C4 |Wn| (θ̃n − θ ) is bounded in probability. C5 l = lim infn ln > 0, where for each n, ln denotes the minimal eigenvalue of S̄n,θ∗(β ...

Arithmetic of K3 surfaces defined over finite fields are investigated. In particular, we show that any K3 surface X of finite height over a finite field k of characteristic p ≥ 5 has a quasi-canonical lifting Z to characteristic 0, and that the endormorphism algebra of the transcendental cycles V (Z), as a Hodge module, is a CM field over Q. We also prove the Tate conjecture for any powers of s...

Using a magnetic Frederiks transition technique, we measure the temperature and concentration dependences of splay K1, twist K2, and bend K3 elastic constants for the lyotropic chromonic liquid crystal sunset yellow formed through noncovalent reversible aggregation of organic molecules in water. K1 and K3 are comparable to each other and are an order of magnitude higher than K2. At higher conce...

We construct a class of geometric twists for Calabi-Yau manifolds of Voisin-Borcea type (K3 × T )/Z2 and study the superpotential in a type IIA orientifold based on this geometry. The twists modify the direct product by fibering the K3 over T 2 while preserving the Z2 involution. As an important application, the Voisin-Borcea class contains T /(Z2 × Z2), the usual setting for intersecting D6 br...

We determine all complex K3 surfaces with Picard rank 20 over Q. Here the NéronSeveri group has rank 20 and is generated by divisors which are defined over Q. Our proof uses modularity, the Artin-Tate conjecture and class group theory. With different techniques, the result has been established by Elkies to show that Mordell-Weil rank 18 over Q is impossible for an elliptic K3 surface. We also a...

<p dir="ltr"><span>Abstrak: </span><span>Kesadaran akan pentingnya menerapkan Kesehatan dan Keselamatan Kerja (K3) di kalangan siswa Sekolah Menengah Kejuruan (SMK) sangat penting ditanamkan sejak awal.</span><span>Penelitian ini bertujuan untuk mengetahui kontribusi dari pengetahuan K3 sikap terhadap kesadaran berperilaku K3. Studi kasus dilaksanakan Program...

In a previous paper, [S2], we described six families of K3-surfaces with Picardnumber 19, and we identified surfaces with Picard-number 20. In these notes we classify some of the surfaces by computing their transcendental lattices. Moreover we show that the surfaces with Picard-number 19 are birational to a Kummer surface which is the quotient of a non-product type abelian surface by an involut...