3 citations · 6 across the 15 of their papers we have counts for
5 papers · 1 filter
Hypergeometric decomposition of Delsarte K3 pencils
Rachel Davis, Jessamyn Dukes, Thais Gomes Ribeiro +4
We study five pencils of projective quartic Delsarte K3 surfaces. Over finite fields, we give explicit formulas for the point counts of each family, written in terms of hypergeomet…
Hasse--Witt matrices and mirror toric pencils
Adriana Salerno, Ursula Whitcher
Mirror symmetry suggests unexpected relationships between arithmetic properties of distinct families of algebraic varieties. For example, Wan and others have shown that for some mi…
Counting points with Berglund-Huebsch-Krawitz mirror symmetry
Ursula Whitcher
We give an expository discussion of recent work using Berglund-Huebsch-Krawitz mirror symmetry to describe the structure of point counts on algebraic varieties over finite fields.
Hypergeometric decomposition of symmetric K3 quartic pencils
Charles F. Doran, Tyler L. Kelly, Adriana Salerno +3
We study the hypergeometric functions associated to five one-parameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picard--Fuchs…
Zeta functions of alternate mirror Calabi-Yau families
Charles F. Doran, Tyler L. Kelly, Adriana Salerno +3
We prove that if two Calabi-Yau invertible pencils have the same dual weights, then they share a common factor in their zeta functions. By using Dwork cohomology, we demonstrate th…