Related papers: K3 Surfaces, Igusa Cusp Form and String Theory

We study K3 surfaces over a number field $k$ which are double covers of extremal rational elliptic surfaces. We provide a list of all elliptic fibrations on certain K3 surfaces together with the degree of a field extension over which each…

Recent progress on the physical states and scattering amplitudes of the $W_3$ string is reviewed with particular emphasis on the relation between this string theory and the Ising model.

Elliptic K3 admit contraction to plane models, the Weierstrass models. We define a higher dimensional notion of Weierstrass models, show that they are compactification of torsors in a unique form, and propose an application to the kahler…

We discuss properties of the Seifert form for simple $K3$ singularities, and of the Picard lattices of families of weighted $K3$ surfaces. We study a collection $\mathcal{M}_{(\rho,\,\delta)}$ of $K3$ surfaces polarized by their Picard…

We show that on every elliptic K3 surface $X$ there are rational curves $(R_i)_{i\in \mathbb{N}}$ such that $R_i^2 \to \infty$, i.e., of unbounded arithmetic genus. Moreover, we show that the union of the lifts of these curves to…

We use lattice theory to study the isogeny class of a K3 surface. Starting from isotropic Brauer classes, we construct isogenies via Kneser method of neighboring lattices. We also determine the fields of definition of isogenous K3 surfaces,…

We present a complete list of extremal elliptic K3 surfaces. There are altogether 325 of them. The first 112 coincides with Miranda-Persson's list for semi-stable ones. The data include the transcendental lattice which determines uniquely…

The isotropic 3-space I^3 which is one of the Cayley--Klein spaces is obtained from the Euclidean space by substituting the usual Euclidean distance with the isotropic distance. In the present paper, we give several classifications on the…

The Gepner model (2)^4 describes the sigma model of the Fermat quartic K3 surface. Moving through the nearby moduli space using conformal perturbation theory, we investigate how the conformal weights of its fields change at first and second…

We review some of the interplay between mirror symmetry and K3 surfaces.

The notion of a K3 spectrum is introduced in analogy with that of an elliptic spectrum and it is shown that there are "enough" K3 spectra in the sense that for all K3 surfaces X in a suitable moduli stack of K3 surfaces there is a K3…

We compute the genus one family Gromov-Witten invariants of K3 surfaces for non-primitive classes. These calculations verify Gottsche-Yau-Zaslow formula for non-primitive classes with index two. Our approach is to use the genus two…

The main outcome of this paper is that the variety VSP(F,10) of presentations of a general cubic form F in 6 variables as a sum of 10 cubes is a smooth symplectic 4-fold obtained a deformation of the Hilbert square of a K3 surface of genus…

The geometrical description of BPS 3-string junction in the F-theory background is given by lifting a string junction in IIB into F-theory and constructing a holomorphic curve in K3 with respect to a special complex structure of K3. The…

We consider the variant of Mirror Symmetry Conjecture for K3 surfaces which relates "geometry" of curves of a general member of a family of K3 with "algebraic functions" on the moduli of the mirror family. Lorentzian Kac--Moody algebras are…

We survey some aspects of the theory of elliptic surfaces and give some results aimed at determining the Picard number of such a surface. For the surfaces considered, this will be equivalent to determining the Mordell-Weil rank of an…

We study certain even-eight curve configurations on a specific class of Jacobian elliptic K3 surfaces with lattice polarizations of rank ten. These configurations are associated with K3 double covers, some of which are elliptic but not…

A precise formula for the elliptic genus of three E-strings is presented. The related refined free energy coincides with the result calculated from topological string on local half K3 Calabi-Yau threefold up to genus twelve. The elliptic…

We classify all the K3 surfaces which are minimal models of the quotient of the product of two curves $C_1\times C_2$ by the diagonal action of either the group $\Z/p\Z$ or the group $\Z/2p\Z$. These K3 surfaces admit a non-symplectic…

We review the relationship between the largest Mathieu group and various modular objects, including recent progress on the relation to mock modular forms. We also review the connections between these mathematical structures and string…