D. Schindler
Published 2013-07-26, updated 2014-05-02Version 2
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.
Manin's conjecture for a quartic del Pezzo surface with A_3 singularity and four lines
Manin's conjecture for integral points on toric varieties
Manin's conjecture for quartic del Pezzo surfaces with a conic fibration
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