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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2016, Issue 714


Manin's conjecture for certain biprojective hypersurfaces

Damaris Schindler
Published Online: 2014-04-25 | DOI: https://doi.org/10.1515/crelle-2014-0026


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.

About the article

Received: 2013-07-29

Revised: 2014-02-05

Published Online: 2014-04-25

Published in Print: 2016-05-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2016, Issue 714, Pages 209–250, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2014-0026.

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