Manin's conjecture for certain biprojective hypersurfaces
Manin's conjecture for certain biprojective hypersurfaces
复制标题
DOI：
10.1515/crelle-2014-0026
复制
发表时间：
2013-07
期刊：
影响因子：
--
通讯作者：
D. Schindler
中科院分区：
文献类型：
--
作者：
D. Schindler
Using the circle method, we count integer points on complete intersections in biprojective space in boxes of different side length, provided the number of variables is large enough depending on the degree of the defining equations and certain loci related to the singular locus. Having established these asymptotics we deduce asymptotic formulas for rational points on such varieties with respect to the anticanonical height function. In particular, we establish a conjecture of Manin for certain smooth hypersurfaces in biprojective space of sufficiently large dimension.
