4 citations · 7 across the 6 of their papers we have counts for
7 papers
Picard-Fuchs equations of families of QM abelian surfaces
Amnon Besser, Ron Livné
We describe an algorithm for computing the Picard-Fuchs equation for a family of twists of a fixed elliptic surface. We then apply this algorithm to obtain the equation for several…
Abelian Varieties with Quaternion Multiplication
Ron Donagi, Ron Livné
In this article we use a Prym construction to study low dimensional abelian varieties with an action of the quaternion group. In special cases we describe the Shimura variety param…
The modularity of certain non-rigid Calabi-Yau threefolds
Ron Livné, Noriko Yui
Let be a Calabi--Yau threefold fibred over by non-constant semi-stable K3 surfaces and reaching the Arakelov--Yau bound. In [STZ], X. Sun, Sh.-L. Tan, and K. Zu…
Local points on P-adically uniformized Shimura varieties
Bruce W. Jordan, Ron Livné, Yakov Varshavsky
Using the p-adic uniformization of Shimura varieties we determine, for some of them, over which local fields they have rational points. Using this we show in some new curve cases t…
The Chord Construction
D. Lehavi, R. Livné
Let F be a smooth plane curve of degree 3. Let \gb be an element in Pic(F)[2]-{0}. Let us define F':={\ol{p(p+\gb)}|p in F}\subset(P^2)^*. In this note we show that F' is a smooth…
The Ramanujan property for regular cubical complexes
Bruce W. Jordan, Ron Livné
This paper considers a higher-dimensional generalization of the notion of Ramanujan graphs, defined by Lubotzky, Phillips, and Sarnak. Specifically the Ramanujan property is studie…