Related papers: Nikulin involutions and the CHL string

Eight-dimensional nongeometric heterotic strings were constructed as duals of F-theory on $\Lambda^{1,1}\oplus E_8\oplus E_7$ lattice polarized K3 surfaces by Malmendier and Morrison. We study the structure of the moduli space of this…

The purpose of this note is twofold. We first review the theory of Fourier-Mukai partners together with the relevant part of Nikulin's theory of lattice embeddings via discriminants. Then we consider Fourier-Mukai partners of K3 surfaces in…

Consider the Jacobian of a genus two curve defined over a finite field and with complex multiplication. In this paper we show that if the l-Sylow subgroup of the Jacobian is not cyclic, then the embedding degree of the Jacobian with respect…

Using results of our papers [19], [20] and [21] about classification of degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups, we classify Picard lattices of Kahlerian K3 surfaces. By classification we understand…

We study smooth curves on abelian surfaces, especially for genus 4, when the complementary subvariety in the Jacobian is also a surface. We show that up to translation there is exactly one genus 4 hyperelliptic curve on a general (1,…

We present a treatment of the algebraic description of the Jacobian of a generic genus two plane curve which exploits an SL2(k) equivariance and clarifes the structure of E.V.Flynn's 72 defining quadratic relations. The treatment is also…

We review quantitative tests on the duality between the heterotic string on T^2 and F-theory on K3. On the heterotic side, certain threshold corrections to the effective action can be exactly computed at one-loop order, and the issue is to…

This paper is concerned with the construction of extremal elliptic K3 surfaces. It gives a complete treatment of those fibrations which can be derived from rational elliptic surfaces by easy manipulations of their Weierstrass equations. In…

We chart the classical moduli space of heterotic strings with broken supersymmetry a la Scherk-Schwarz and gauge group rank reduced by 8 in eight dimensions. This space consists of four connected components, each with its own characteristic…

We classify Enriques involutions on a K3 surface, up to conjugation in the automorphism group, in terms of lattice theory. We enumerate such involutions on singular K3 surfaces with transcendental lattice of discriminant smaller than or…

We compute explicit rational models for some Hilbert modular surfaces corresponding to square discriminants, by connecting them to moduli spaces of elliptic K3 surfaces. Since they parametrize decomposable principally polarized abelian…

We investigate a notion of "higher modularity" for elliptic curves over function fields. Given such an elliptic curve $E$ and an integer $r\geq 1$, we say that $E$ is $r$-modular when there is an algebraic correspondence between a stack of…

In previous work, we have introduced a program aimed at studying the birational geometry of locally symmetric varieties of Type IV associated to moduli of certain projective varieties of K3 type. In particular, a concrete goal of our…

We investigate infinite distance limits in the complex structure moduli space of F-theory compactified on K3 to eight dimensions. While this is among the simplest possible arenas to test ideas about the Swampland Distance Conjecture, it is…

Double planes branched in 6 lines give a famous example of K3 surfaces. Their moduli are well understood and related to abelian fourfolds of Weil type. We compare these two moduli interpretations and in particular divisors on the moduli…

In this paper we study genus 2 curves whose Jacobians admit a polarized (4,4)-isogeny to a product of elliptic curves. We consider base fields of characteristic different from 2 and 3, which we do not assume to be algebraically closed. We…

We show that any polarized K3 surface supports special Ulrich bundles of rank 2.

We study threefolds X in a projective space having as hyperplane section a smooth surface with an elliptic fibration. We first give a general theorem about the possible embeddings of such surfaces with Picard number two. More precise…

We consider K3 surfaces which are double cover of rational elliptic surfaces. The former are endowed with a natural elliptic fibration, which is induced by the latter. There are also other elliptic fibrations on such K3 surfaces, which are…

It has been recently shown that F-theory on K3 with background B fields (NSNS and RR 2-forms) is dual to the CHL string in 8 dimensions. In this paper, we reexamine this duality in terms of string junctions in type IIB string theory. It is…