We show that every Picard rank one smooth Fano threefold has a weak Landau–Ginzburg
model coming from a toric degeneration. The fibers of these Landau–Ginzburg models can …

Calabi-Yau manifolds are compact, complex Kähler manifolds that have trivial first Chern
classes (over R). In most cases, we assume that they have finite fundamental groups. By the …

In this thesis we address several questions around mirror symmetry for Fano manifolds and
Calabi-Yau varieties. Fano mirror symmetry is a relationship between a Fano manifold X and …

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 …

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 …

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 smooth …

In this article we introduce a collection of partial differential equations in the moduli of lattice
polarized K3 surfaces whose algebraic solutions are the loci of K3 surfaces with lattice …

Calabi-Yau threefolds realized as anticanonical hypersurfaces or complete intersections in
toric varieties. Our attention to these families is motivated by the Doran-Morgan classification …

The guiding principle in this monograph is to develop a new theory of modular forms which
encompasses most of the available theory of modular forms in the literature, such as those …

Abstract Using Gauss–Manin derivatives of generalized normal functions, we arrive at
results on the non-triviality of the transcendental regulator for K m of a very general …