Weak approximation over function fields
We prove that rationally connected varieties over the function field of a complex curve satisfy weak approximation for places of good reduction.
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arXiv subjects
Yuri Tschinkel
Publications and source records attributed to Yuri Tschinkel.
On the arithmetic of del Pezzo surfaces of degree 2
We study the arithmetic of certain del Pezzo surfaces of degree 2. We produce examples of Brauer-Manin obstruction to the Hasse principle, coming from 2- and 4-torsion elements in the Brauer group.
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Reconstruction of function fields
We study the structure of abelian subgroups of Galois groups of function fields of surfaces.
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Rational curves and points on K3 surfaces
We study the distribution of algebraic points on K3 surfaces.
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Universal torsors and Cox rings
We study the equations of universal torsors on rational surfaces.
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Special elliptic fibrations
We construct examples of elliptic fibrations of orbifold general type (in the sense of Campana) which have no etale covers dominating a variety of general type.
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Integral points and effective cones of moduli spaces of stable maps
Consider the Fulton-MacPherson configuration space of $n$ points on $¶^1$, which is isomorphic to a certain moduli space of stable maps to $¶^1$. We compute the cone of effective ${\mathfrak S}_n$-invariant divisors on this space. This yields a geometric interpretation of known asymptotic formulas for the number of integral points of bounded height on compactifications of $\SL_2$ in the space of binary forms of degree $n\ge 3$.
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Rationality of moduli of elliptic fibrations with fixed monodromy
We prove rationality results for moduli spaces of elliptic K3 surfaces and elliptic rational surfaces with fixed monodromy groups.
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Height zeta functions of equivariant compactifications of the Heisenberg group
We study analytic properties of height zeta functions of equivariant compactifications of the Heisenberg group.
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Simple examples of symplectic fourfolds with exotic properties
We construct examples of simply connected nonalgebraic symplectic fourfolds with a prescribed number of nonintersecting symplectic curves with positive self-intersections.
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Unramified correspondences
We study correspondences between algebraic curves defined over the separable closure of $\Q$ or $\F_p$.
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On the effective cone of the moduli space of pointed rational curves
We compute the effective cone for the moduli space of stable rational curves with at most six marked points.
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On the distribution of points of bounded height on equivariant compactifications of vector groups
We prove asymptotic formulas for the number of rational points of bounded height on smooth equivariant compactifications of the affine space. (Nous établissons un développement asymptotique du nombre de points rationnels de hauteur bornée sur les compactifications équivariantes lisses de l'espace affine.)
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Commuting elements in Galois groups of function fields
We study abelian subgroups of Galois groups of function fields.
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Lagrangian subvarieties of abelian fourfolds
We construct examples of algebraic surfaces with interesting fundamental groups.
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Density of integral points on algebraic varieties
We study the distribution of integral points on log varieties.
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Fonctions zêta des hauteurs des espaces fibrés
This paper is devoted to the estimation of the number of points of bounded height on fibrations in toric varieties over algebraic varieties, generalizing previous work by Strauch and the second author. Under reasonable hypotheses on ``Arakelov L-functions'' of the base, we show how to deduce a good estimate for the open subset of the total space of the unerlying fibration in torus. In passing, we improve drastically the error term for toric varieties themselves, generalizing a theorem by de la Breteche over any number field.
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Monodromy of elliptic surfaces
We study monodromy groups of elliptic fibrations over the projective line.
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