Manin's conjecture for certain biprojective hypersurfaces
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Damaris Schindler
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.
The author would like to thank Professor T. D. Wooley for suggesting this area of research, the referee for his or her comments and Professor T. D. Browning for useful discussions. The author is grateful to Professor P. Salberger for providing the proof of Theorem 2.4 and for useful comments.
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Matrix factorizations and cohomological field theories
- On the irreducibility of locally metric connections
- A congruence modulo four in real Schubert calculus
- Some remarks concerning the Grothendieck period conjecture
- Manin's conjecture for certain biprojective hypersurfaces
Articles in the same Issue
- Frontmatter
- Matrix factorizations and cohomological field theories
- On the irreducibility of locally metric connections
- A congruence modulo four in real Schubert calculus
- Some remarks concerning the Grothendieck period conjecture
- Manin's conjecture for certain biprojective hypersurfaces
