16 citations · 101 across the 15 of their papers we have counts for
17 papers
Irrational families of Fano weighted complete intersection fourfolds
Jiaji Cai, Andrew Harder, Sukjoo Lee
We study the irrationality of smooth Fano complete intersection fourfolds in weighted projective spaces, using an atom theoretic approach based solely on Gromov--Witten invariants.…
Modularity of Landau-Ginzburg models
Charles Doran, Andrew Harder, Ludmil Katzarkov +2
For each Fano threefold, we construct a family of Landau-Ginzburg models which satisfy many expectations coming from different aspects of mirror symmetry; they are log Calabi-Yau v…
Motivic geometry of two-loop Feynman integrals
Charles F. Doran, Andrew Harder, Eric Pichon-Pharabod +1
We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached…
Mixed Hodge structures in log symplectic geometry
Andrew Harder
We study the cohomology rings of snc log symplectic pairs which have log symplectic forms of pure weight. We show that under a certain natural condition, the cohomology rin…
P=W for Lagrangian fibrations and degenerations of hyper-Kähler manifolds
Andrew Harder, Zhiyuan Li, Junliang Shen +1
We identify the perverse filtration of a Lagrangian fibration with the monodromy weight filtration of a maximally unipotent degeneration of compact hyper-Kähler manifolds.
Torus fibers and the weight filtration
Andrew Harder
We show that if is a simple normal crossings log Calabi--Yau pair, then there is a real torus of dimension equal to the codimension of the smallest stratum of which can…
Pseudolattices, del Pezzo surfaces, and Lefschetz fibrations
Andrew Harder, Alan Thompson
Motivated by the relationship between numerical Grothendieck groups induced by the embedding of a smooth anticanonical elliptic curve into a del Pezzo surface, we define the notion…
Perverse sheaves of categories and some applications
Andrew Harder, Ludmil Katzarkov
We study perverse sheaves of categories their connections to classical algebraic geometry. We show how perverse sheaves of categories encode naturally derived categories of coheren…
Hodge numbers of Landau-Ginzburg models
Andrew Harder
We study the Hodge numbers of Landau-Ginzburg models as defined by Katzarkov, Kontsevich and Pantev. First we show that these numbers can be computed using ordinary mixed Hodge the…
Calabi-Yau threefolds fibred by high rank lattice polarized K3 surfaces
Charles F. Doran, Andrew Harder, Andrey Y. Novoseltsev +1
We study threefolds fibred by K3 surfaces admitting a lattice polarization by a certain class of rank 19 lattices. We begin by showing that any family of such K3 surfaces is comple…
Hodge Numbers from Picard-Fuchs Equations
Charles F. Doran, Andrew Harder, Alan Thompson
Given a variation of Hodge structure over with Hodge numbers , we show how to compute the degrees of the Deligne extension of its Hodge bundles, follo…
Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds
Charles F. Doran, Andrew Harder, Alan Thompson
We investigate a potential relationship between mirror symmetry for Calabi-Yau manifolds and the mirror duality between quasi-Fano varieties and Landau-Ginzburg models. More precis…
Toric Degenerations and the Laurent polynomials related to Givental's Landau-Ginzburg models
Andrew Harder, Charles F. Doran
For an appropriate class of Fano complete intersections in toric varieties, we prove that there is a concrete relationship between degenerations to specific toric subvarieties and…
The Geometry and Moduli of K3 Surfaces
Andrew Harder, Alan Thompson
These notes will give an introduction to the theory of K3 surfaces. We begin with some general results on K3 surfaces, including the construction of their moduli space and some of…
Calabi-Yau Threefolds Fibred by Kummer Surfaces Associated to Products of Elliptic Curves
Charles F. Doran, Andrew Harder, Andrey Y. Novoseltsev +1
We study threefolds fibred by Kummer surfaces associated to products of elliptic curves, that arise as resolved quotients of threefolds fibred by certain lattice polarized K3 surfa…
Calabi-Yau Threefolds Fibred by Mirror Quartic K3 Surfaces
Charles F. Doran, Andrew Harder, Andrey Y. Novoseltsev +1
We study threefolds fibred by mirror quartic K3 surfaces. We begin by showing that any family of such K3 surfaces is completely determined by a map from the base of the family to t…
Families of lattice polarized K3 surfaces with monodromy
Charles F. Doran, Andrew Harder, Andrey Y. Novoseltsev +1
We extend the notion of lattice polarization for K3 surfaces to families over a (not necessarily simply connected) base, in a way that gives control over the action of monodromy on…