57 citations · 359 across the 40 of their papers we have counts for
31 papers · 1 filter
Some applications of the moduli space of -polarized K3 surfaces
Adrian Clingher, Andreas Malmendier, Brandon Williams
We study K3 surfaces polarized by the lattice through elliptic fibrations and orthogonal modular forms. Using an alternate genus-one fibration and its relative Ja…
On the Vinberg Family of K3 Surfaces
Adrian Clingher, Andreas Malmendier, Brandon Williams
We study orthogonal modular forms associated with moduli spaces of lattice-polarized K3 surfaces whose generic transcendental lattices are of the form …
Kummer Surfaces, Isogenies and Theta Functions
Adrian Clingher, Andreas Malmendier, Tony Shaska
The paper discusses geometric and computational aspects associated with -isogenies for principally polarized Abelian surfaces and related Kummer surfaces. We start by review…
K3 Surfaces and Orthogonal Modular Forms
Adrian Clingher, Andreas Malmendier, Brandon Williams
We determine explicit generators for the ring of modular forms associated with the moduli spaces of K3 surfaces with automorphism group and of Picard r…
Twists, Eisenstein series, and Instantons in Local Mirror Symmetry
Andreas Malmendier, Michael T. Schultz
We propose a mechanism for computing the genus zero invariants of local Calabi-Yau fourfolds arising as the total space of the canonical bundle of a rank-1 Fano threefold. Our meth…
On holomorphic conformal structures associated with lattice polarized K3 surfaces
Andreas Malmendier, Michael T. Schultz
We discuss the connection between Picard-Fuchs equations for certain families of lattice polarized K3 surfaces and the construction of integrable holomorphic conformal structures o…
On projective K3 surfaces with
Adrian Clingher, Andreas Malmendier, Xavier Roulleau
We prove that every K3 surface with automorphism group admits an explicit birational model as a double sextic surface. This model is canonical for Pica…
On two-elementary K3 surfaces with finite automorphism group
Adrian Clingher, Andreas Malmendier, Flora Poon
We study complex algebraic K3 surfaces of Picard ranks 11,12, and 13 of finite automorphism group that admit a Jacobian elliptic fibration with a section of order two. We prove tha…
The duality between F-theory and the Heterotic String in with two Wilson lines
Adrian Clingher, Thomas Hill, Andreas Malmendier
We construct non-geometric string compactifications by using the F-theory dual of the heterotic string compactified on a two-torus with two Wilson line parameters, together with a…
On the duality of F-theory and the CHL string in seven dimensions
Adrian Clingher, Andreas Malmendier
We show that the duality between F-theory and the CHL string in seven dimensions defines algebraic correspondences between K3 surfaces polarized by the rank-ten lattices $H \oplus…
Isogenies of certain K3 surfaces of rank 18
Noah Braeger, Adrian Clingher, Andreas Malmendier +1
We construct geometric isogenies between three types of two-parameter families of K3 surfaces of Picard rank 18. One is the family of Kummer surfaces associated with Jacobians of g…
On Néron-Severi lattices of Jacobian elliptic K3 surfaces
Adrian Clingher, Andreas Malmendier
We classify all Jacobian elliptic fibrations on K3 surfaces with finite automorphism group. We also classify all Jacobian elliptic fibrations with finite Mordell-Weil group on K3 s…
On the mixed-twist construction and monodromy of associated Picard-Fuchs systems
Andreas Malmendier, Michael T. Schultz
We use the mixed-twist construction of Doran and Malmendier to obtain a multi-parameter family of K3 surfaces of Picard rank . Upon identifying a particular Jacobian ellip…
On K3 surfaces of Picard rank 14
Adrian Clingher, Andreas Malmendier
We study complex algebraic K3 surfaces with finite automorphism groups and polarized by rank-fourteen, 2-elementary lattices. Three such lattices exist, namely $H \oplus E_8(-1) \o…
Geometry of Prym varieties for special bielliptic curves of genus three and five
Adrian Clingher, Andreas Malmendier, Tony Shaska
We construct two pencils of bielliptic curves of genus three and genus five. The first pencil is associated with a general abelian surface with a polarization of type . The…
Kummer sandwiches and Greene-Plesser construction
Noah Braeger, Andreas Malmendier, Yih Sung
In the context of K3 mirror symmetry, the Greene-Plesser orbifolding method constructs a family of K3 surfaces, the mirror of quartic hypersurfaces in , starting from…
Jacobian elliptic fibrations on the generalized Inose quartic of Picard rank sixteen
Adrian Clingher, Thomas Hill, Andreas Malmendier
We consider the family of complex algebraic K3 surfaces with Picard lattice containing the unimodular lattice . The surface $\mathcal…
From hyperelliptic to superelliptic curves
Andreas Malmendier, Tony Shaska
In this long survey article we show that the theory of elliptic and hyperelliptic curves can be extended naturally to all superelliptic curves. We focus on automorphism groups, str…
Rational points in the moduli space of genus two
L. Beshaj, R. Hidalgo, S. Kruk +3
We build a database of genus 2 curves defined over which contains all curves with minimal absolute height , all curves with moduli height $\mathfrak h \leq 20…
Counting Rational Points on Kummer surfaces
Andreas Malmendier, Yih Sung
We consider the problem of counting the number of rational points on the family of Kummer surfaces associated with two non-isogenous elliptic curves. For this two-parameter family…
On isogenies among certain abelian surfaces
Adrian Clingher, Andreas Malmendier, Tony Shaska
We construct a three-parameter family of non-hyperelliptic and bielliptic plane genus-three curves whose associated Prym variety is two-isogenous to the Jacobian variety of a gener…
Normal forms for Kummer surfaces
Adrian Clingher, Andreas Malmendier
We determine normal forms for the Kummer surfaces associated with abelian surfaces of polarization of type , , , , and . Explicit formulas for co…
Six line configurations and string dualities
Adrian Clingher, Andreas Malmendier, Tony Shaska
We study the family of K3 surfaces of Picard rank sixteen associated with the double cover of the projective plane branched along the union of six lines, and the family of its Van…
Nikulin involutions and the CHL string
Adrian Clingher, Andreas Malmendier
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 wi…