Manin's conjecture for certain biprojective hypersurfaces

2013/07/26 by Damaris Schindler, Schindler, D. · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.1307.7069

Abstract

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.

Citations

• Rational points of bounded height on Fano varieties

Cited by

• Solubility of a family of conics with polynomial coefficients in many variables
• Rational points on varieties defined by multihomogeneous diagonal forms

Related

• Manin's conjecture for toric varieties
• Points de hauteur bornée sur les hypersurfaces lisses des variétés toriques. Cas général
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