Density of rational points on a quadric bundle in P 3 × P 3

Autor:	Tim D Browning, D. R. Heath-Brown
Rok vydání:	2020
Předmět:	Pure mathematics Quadric Conjecture Geometry of numbers General Mathematics 010102 general mathematics 01 natural sciences Hypersurface Bounded function Bundle 0103 physical sciences Asymptotic formula 010307 mathematical physics 0101 mathematics Variety (universal algebra) Mathematics
Zdroj:	Duke Mathematical Journal. 169
ISSN:	0012-7094
DOI:	10.1215/00127094-2020-0031
Popis:	We establish an asymptotic formula for the number of rational points of bounded anticanonical height which lie on a certain Zariski-dense subset of the biprojective hypersurface x 1 y 2 1 + ⋯ + x 4 y 2 4 = 0 in P 3 × P 3 . This confirms the modified Manin conjecture for this variety, in which the removal of a “thin” set of rational points is allowed.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::45aa0e5253bc49f1f06254cec707b1a3 https://doi.org/10.1215/00127094-2020-0031 Zobrazit plný text záznamu