ABELIAN FIBRATIONS AND RATIONAL POINTS ON SYMMETRIC PRODUCTS

DOI10.1142/S0129167X00000544zbMath0982.14012arXivmath/9909074OpenAlexW2170757394MaRDI QIDQ2706846

Yuri Tschinkel, Brendan Hassett

Publication date: 16 July 2001

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9909074

zbMATH Keywords

\(K3\) surfacesabelian fibrationsZariski dense rational pointsAbelian fibrationsymmetric product of a \(K3\) surface

Mathematics Subject Classification ID

Rational points (14G05) (K3) surfaces and Enriques surfaces (14J28) Fibrations, degenerations in algebraic geometry (14D06) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20)

Related Items

Lagrangian fibrations on Hilbert schemes of points on K3 surfaces ⋮ On the distribution of rational points on ramified covers of abelian varieties ⋮ On families of rational curves in the Hilbert square of a surface ⋮ Two remarks on sextic double solids ⋮ Birational geometry of Beauville-Mukai systems. I: The rank three and genus two case. ⋮ Birational maps of moduli spaces of vector bundles on \(K3\) surfaces ⋮ Zariski density of points with maximal arithmetic degree ⋮ Prime Fano threefolds and integrable systems ⋮ The Lang–Vojta Conjectures on Projective Pseudo-Hyperbolic Varieties ⋮ An integrable system of \(K3\)-Fano flags ⋮ Arithmetic hyperbolicity: automorphisms and persistence ⋮ Rational Lagrangian fibrations on punctual Hilbert schemes of \(K3\) surfaces ⋮ The generalized Franchetta conjecture for some hyperkähler fourfolds ⋮ Fibrations on four-folds with trivial canonical bundles ⋮ Rational points and ramified covers of products of two elliptic curves ⋮ Hyperbolicity and specialness of symmetric powers

Cites Work

• Variétés kähleriennes dont la première classe de Chern est nulle
• Description de Hilb sup(n) C{X,Y}
• On fibre space structures of a projective irreducible symplectic manifold
• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• BPS states, string duality, and nodal curves on \(K3\)
• Counting rational curves on \(K3\) surfaces
• Projective Models of K - 3 Surfaces
• On the density of rational points on elliptic fibrations
• Approximation Theory and the Rank of Abelian Varieties Over Large Algebraic Fields