3 citations · 9 across the 17 of their papers we have counts for
18 papers
Special Loci in the Moduli of Curves
David Urbanik, Ziquan Yang
We introduce new techniques to study mixed-characteristic special loci in moduli spaces and give several applications, focusing in particular on the moduli space of…
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 gen…
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 ,…
Degrees of Hodge Loci
David Urbanik
We prove asymptotic estimates for the growth in the degree of the Hodge locus in terms of arithmetic properties of the integral vectors that define it. Our methods are general and…
Effective atypical intersections and applications to orbit closures
Gregorio Baldi, David Urbanik
We propose a new unifying setting for dealing with monodromically atypical intersections that goes beyond the usual Zilber-Pink conjecture. In particular, we give a new proof of fi…
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{…
Existence and density of typical Hodge loci
Nazim Khelifa, David Urbanik
Motivated by a question of Baldi-Klingler-Ullmo, we provide a general sufficient criterion for the existence and analytic density of typical Hodge loci associated to a polarizable…
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…
Unlikely Intersections with Bruhat Strata
David Urbanik
Let be the moduli space of -dimensional principally polarized abelian varieties over , and let be a closed lo…
Algebraic Cycle Loci at the Integral Level
David Urbanik
Let be a smooth projective family defined over , where is a number field and is a finite set o…
Effective Methods for Diophantine Finiteness
David Urbanik
Let be a number field, and let be its ring of -integers. Recently, Lawrence and Venkatesh proposed a general…
Sets of Special Subvarieties of Bounded Degree
David Urbanik
Let be a family of smooth projective algebraic varieties over a smooth connected quasi-projective base , and let be the i…
On the Transcendence of Period Images
David Urbanik
Let be a family of smooth projective algebraic varieties over a smooth connected base , with everything defined over . Denote by $\mathbb{V}…
Absolute Hodge and -adic Monodromy
David Urbanik
Let be a motivic variation of Hodge structure on a -variety , let be the associated -algebraic Hodge bundle, and let $σ\in \textrm{Aut}(\mathbb{…
On the fields of definition of Hodge loci
Bruno Klingler, Anna Otwinowska, David Urbanik
A polarizable variation of Hodge structure over a smooth complex quasi projective variety is said to be defined over a number field if and the algebraic connection asso…
Explicit Rational Group Law on Hyperelliptic Jacobians of any Genus
David Urbanik
It is well-known that abelian varieties are projective, and so that there exist explicit polynomial and rational functions which define both the variety and its group law. It is ho…