16 citations · 96 across the 19 of their papers we have counts for
20 papers
Degenerations and Fibrations of K3 Surfaces: Lattice Polarisations and Mirror Symmetry
Luca Giovenzana, Alan Thompson
Tyurin degenerations of K3 surfaces are degenerations whose central fibre consists of a pair of rational surfaces glued along a smooth elliptic curve. We study the lattice theory o…
Normal Forms and Tyurin Degenerations of K3 Surfaces Polarised by a Rank 18 Lattice
Charles F. Doran, Joseph Prebble, Alan Thompson
We study projective Type II degenerations of K3 surfaces polarised by a certain rank 18 lattice, where the central fibre consists of a pair of rational surfaces glued along a smoot…
K-moduli of Fano threefolds in family 3.10
Ivan Cheltsov, Alan Thompson
We find all K-polystable limits of smooth Fano threefolds in family 3.10.
The Mirror Clemens-Schmid Sequence
Charles F. Doran, Alan Thompson
We introduce a four-term long exact sequence that relates the cohomology of a smooth variety admitting a projective morphism onto a projective base to the cohomology of the open se…
Threefolds Fibred by Mirror Sextic Double Planes
Remkes Kooistra, Alan Thompson
We present a systematic study of threefolds fibred by K3 surfaces that are mirror to sextic double planes. There are many parallels between this theory and the theory of elliptic s…
Stable pair compactification of moduli of K3 surfaces of degree 2
Valery Alexeev, Philip Engel, Alan Thompson
We prove that the universal family of polarized K3 surfaces of degree 2 can be extended to a flat family of stable slc pairs over the toroidal compactification associated…
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…
ADE surfaces and their moduli
Valery Alexeev, Alan Thompson
We define a class of surfaces corresponding to the ADE root lattices and construct compactifications of their moduli spaces as quotients of projective varieties for Coxeter fans, g…
Mirror Symmetry for Lattice Polarized del Pezzo Surfaces
Charles F. Doran, Alan Thompson
We describe a notion of lattice polarization for rational elliptic surfaces and weak del Pezzo surfaces, and describe the complex moduli of the former and the Kähler cone of the la…
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…
An Introduction to Hodge Structures
Sara Angela Filippini, Helge Ruddat, Alan Thompson
We begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, whi…
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…
The 14th case VHS via K3 fibrations
Adrian Clingher, Charles F. Doran, Jacob Lewis +2
We present a study of certain singular one-parameter subfamilies of Calabi-Yau threefolds realized as anticanonical hypersurfaces or complete intersections in toric varieties. Our…
Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two
Alan Thompson
We consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarisation of degree two on the general fib…
Degenerations of K3 Surfaces of Degree Two
Alan Thompson
We consider a semistable degeneration of K3 surfaces, equipped with an effective divisor that defines a polarisation of degree two on a general fibre. We show that the map to the r…