On the distribution of points of bounded height on equivariant compactifications of vector groups
By Antoine Chambert-Loir, Yuri Tschinkel. 2000
128 citations recorded by the source corpus.
Abstract.We prove asymptotic formulas for the number of rational points of bounded height on smooth equivariant compactifications of the affine space.
Subfields: Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/780899d7946fa8f5d2ded55d500a527b25817afb
How researchers see this paper
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In Mathematical Physics
- A. Nevo
- Alexander Gorodnik
- Ulrich Derenthal
- Antoine Chambert-Loir
- Yuri Tschinkel
- Tim D Browning
- Sho Tanimoto
- Brian Lehmann
Citations in the corpus
- Rational Points on Compactifications of Semi-Simple Groups of Rank 1 (2006, background): “RATIONAL POINTS 3 papers [6], [37], [ 14 ] and [31].”
- Integral points of bounded height on partial equivariant compactifications of vector groups (2009, methodology): “3 of [3], this finiteness property still holds.”
- Singular del Pezzo surfaces whose universal torsors are hypersurfaces (2006, background): “— 6 Toric [7] A1 4 Toric [7] A1 3 1 relation [21, 26] 2A1 2 Toric [7] A2 2 1 relation [26, 60] A2 + A1 1 Toric [7]”
- On Manin's conjecture for singular del Pezzo surfaces of degree four, II (2004, background): “It turns out that X is an equivariant compactification of G2a, so that the work of Chambert-Loir and Tschinkel [5, Theorem 0.1] ensures that the asymptotic formula (1.1) holds when U ⊂ X is taken to be the open subset formed by deleting the unique line from X .”
- Geometric consistency of Manin's conjecture (2018, background): “There are a few important classes of varieties for which the a, binvariants for big line bundles do indeed agree with point growth rates: for example, when the variety is a toric variety [BT96a] or an equivariant compactification of a vector group [CLT02].”
- Counting lattice points (2009, background): “(1) Via direct spectral expansion and regularisation of the automorphic kernel on G=G, G semisimple [3], [4], [14], [17], [25], [26], [31], [49], [55], [56], [74], [63], [77], [85], [83], [84], [82],”