Manin's conjecture for certain spherical threefolds

authored by

Ulrich Derenthal, Giuliano Gagliardi

Abstract

We prove Manin's conjecture on the asymptotic behavior of the number of rational points of bounded anticanonical height for a spherical threefold with canonical singularities and two infinite families of spherical threefolds with log terminal singularities. Moreover, we show that one of these families does not satisfy a conjecture of Batyrev and Tschinkel on the leading constant in the asymptotic formula. Our proofs are based on the universal torsor method, using Brion's description of Cox rings of spherical varieties.

Organisation(s)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

External Organisation(s)

Tel Aviv University

Type

Artikel

Journal

Advances in mathematics

Volume

337

Pages

39-82

No. of pages

44

ISSN

0001-8708

Publication date

15.10.2018

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Mathematik (insg.)

Electronic version(s)

https://doi.org/10.48550/arXiv.1611.04754 (Access: Offen)
https://doi.org/10.1016/j.aim.2018.08.005 (Access: Geschlossen)