Height zeta functions of toric varieties

DOI10.1007/BF02362469zbMath0915.14013arXivalg-geom/9606003OpenAlexW1972319484MaRDI QIDQ1356322

Victor V. Batyrev, Yuri Tschinkel

Publication date: 6 November 1997

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9606003

zbMATH Keywords

toric varietiesheight zeta functioneffective divisorsnumber of rational points of bounded height

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Divisors, linear systems, invertible sheaves (14C20)

Related Items (19)

Distribution of rational points of bounded height on equivariant compactifications of \(\mathrm{PGL}_2\). I ⋮ Endomotives of toric varieties ⋮ On the Hilbert property and the fundamental group of algebraic varieties ⋮ Geometric consistency of Manin's conjecture ⋮ On upper bounds of Manin type ⋮ Hyperbola method on toric varieties ⋮ Points of bounded height, adelic topology and Tamagawa measures. ⋮ Fonction zêta des hauteurs des variétés toriques non déployées ⋮ Points of bounded height on equivariant compactifications of vector groups. II ⋮ Counting points on a toric variety ⋮ Rational points on homogeneous varieties and equidistribution of adelic periods (with appendix by Mikhail Borovoi) ⋮ Rational points in flag varieties over function fields ⋮ Manin's conjecture and the Fujita invariant of finite covers ⋮ Height zeta functions ⋮ Algebraic points, non-anticanonical heights and the Severi problem on toric varieties ⋮ On exceptional sets in Manin's conjecture ⋮ Number of points of bounded height on del Pezzo surfaces of degree 5 ⋮ Distribution of rational points on toric varieties: all the heights ⋮ Campana points on biequivariant compactifications of the Heisenberg group

Cites Work

• On the Phragmén-Lindelöf theorem and some applications
• On the number of rational points of bounded height on algebraic varieties
• Heights and Tamagawa measures on Fano varieties
• \(L\)-functions of algebraic tori
• Arithmetic of algebraic tori
• On the Tamagawa number of algebraic tori
• Positivitatsbereiche Im R n
• PROJECTIVE INVARIANT DEMAZURE MODELS
• THE GEOMETRY OF TORIC VARIETIES
• Rational Points of Bounded Height on Compactifications of Anisotropic Tori
• Domains of positivity
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Height zeta functions of toric varieties