8 papers
Algebraic Hodge generic points are dense
Gregorio Baldi, Gal Binyamini, David Urbanik
Let be a quasi-projective family of varieties defined over . We show that the points of that are H…
Intersections and the Bézout Range: Abelian Varieties
Gregorio Baldi, David Urbanik
Given subvarieties of a complex algebraic variety of complementary dimension, must they intersect? When is projective space, this is a consequence of the classical B…
Galois Orbit Bounds for Surface Degenerations
David Urbanik
Given a smooth proper family of surfaces over a number field , with an irreducible curve and its generic point, we consider the ge…
Arithmetic Deformation of Line Bundles
David Urbanik, Ziquan Yang
We introduce a new method to study mixed characteristic deformation of line bundles. In particular, for sufficiently large smooth projective families $f : \mathscr{X} \to \mathscr{…
On the Complexity of Atypical Special Points
David Urbanik
Given an integral variation of Hodge structure on a complex algebraic variety , polarized by some bilinear form ,…
Geometric G-functions and Atypicality
David Urbanik
We describe a general method for giving -adic interpretations of -functions arising from degenerating periods of smooth projective algebraic varieties. Using this, we are abl…