Abstract
AbstractInspired by a method of La Bretèche relying on some unique factorisation, we generalise work of Blomer, Brüdern and Salberger to prove Manin's conjecture in its strong form conjectured by Peyre for some infinite family of varieties of higher dimension. The varieties under consideration in this paper correspond to the singular projective varieties defined by the following equation$$ x_1 y_2y_3\cdots y_n+x_2y_1y_3 \cdots y_n+ \cdots+x_n y_1 y_2 \cdots y_{n-1}=0 $$in ℙℚ2n−1for alln⩾ 3. This paper comes with an Appendix by Per Salberger constructing a crepant resolution of the above varieties.
Publisher
Cambridge University Press (CUP)
Reference38 articles.
1. The homogeneous coordinate ring of a toric variety;Cox;J. Alg. Geom.,1995
2. Height zeta functions of equivariant compactifications of semi-direct products of algebraic groups
3. Tamagawa numbers of universal torsors and points of bounded height on Fano varieties;Salberger;Nombre et répartition de points de hauteur bornée. Astérisque,1998
4. Chapters on algebraic surfaces
5. Points de hauteur bornée, topologie adélique et mesures de Tamagawa
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献