18 citations · 39 across the 6 of their papers we have counts for
7 papers
On the motive of Kummer varieties associated to - Supplement to the paper: The modularity of certain non-rigid Calabi-Yau threefolds (by R. Livné and N. Yui)
Klaus Hulek, Helena Verrill
In their paper Livné and Yui (math.AG/0304497) discuss several examples of non-rigid Calabi-Yau varieties which admit semi-stable K3-fibrations with 6 singular fibres over a base w…
On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces
Klaus Hulek, Helena Verrill
We prove that (not necessarily rigid) Calabi-Yau threefolds defined over the rationals which contain sufficiently many elliptic ruled surfcaes are modular (under mild restrictions…
Sums of squares of binomial coefficients, with applications to Picard-Fuchs equations
H. A. Verrill
For a fixed integer N, and fixed numbers b_1,...,b_N, we consider sequences, the nth term (a_n) of which is the sum of the squares of the terms in the expansion of (b_1 + ... + b_N…
On modular mod Galois representations with exceptional images
Ian Kiming, Helena A. Verrill
We give a parametrization of the possible Serre invariants of modular mod Galois representations of the exceptional types , , , in terms of local da…
On modularity of rigid and nonrigid Calabi-Yau varieties associated to the root lattice A_4
Klaus Hulek, Helena Verrill
We prove the modularity of four rigid and three nonrigid Calabi-Yau threefolds associated with the root lattice A_4.
Notes on toric varieties
Helena Verrill, David Joyner
These notes survey some basic results in toric varieties over a field with examples and applications. A computer algebra package (written by the second author) is described which d…