69 citations · 615 across the 125 of their papers we have counts for
7 papers · 1 filter
Reconstruction of higher-dimensional function fields
Fedor Bogomolov, Yuri Tschinkel
We prove that function fields of varieties of dimension at least two over an algebraic closure of a finite field are determined, modulo purely inseparable extensions, by the quotie…
Integral points of bounded height on partial equivariant compactifications of vector groups
Antoine Chambert-Loir, Yuri Tschinkel
We establish asymptotic formulas for the number of integral points of bounded height on partial equivariant compactifications of vector groups.
Intersection numbers of extremal rays on holomorphic symplectic varieties
Brendan Hassett, Yuri Tschinkel
We propose a general framework governing the intersection properties of extremal rays of irreducible holomorphic symplectic manifolds under the Beauville-Bogomolov form. Our main t…
Igusa integrals and volume asymptotics in analytic and adelic geometry
Antoine Chambert-Loir, Yuri Tschinkel
We establish asymptotic formulae for volumes of height balls in analytic varieties over local fields and in adelic points of algebraic varieties over number fields, relating the Me…
Constructing rational curves on K3 surfaces
Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel
We develop a mixed-characteristic version of the Mori-Mukai technique for producing rational curves on K3 surfaces. We reduce modulo p, produce rational curves on the resulting K3…
Milnor K_2 and field homomorphisms
Fedor Bogomolov, Yuri Tschinkel
We prove that the function field of an algebraic variety of dimension greater than 1 over an algebraically closed field of characteristic zero is determined by its first and second…
Co-fibered products of algebraic curves
Fedor Bogomolov, Yuri Tschinkel
We give examples of failure of the existence of co-fibered products in the category of algebraic curves.