Weak approximation and rationally connected varieties over function fields of curves
type: Item
instance of: scholarly article
zbMATH Open document ID: 1256.14051
author: Brendan Hassett
publication date: 2012-09-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/1008.2711
Mathematics Subject Classification ID: 14M22
Mathematics Subject Classification ID: 14G05
Mathematics Subject Classification ID: 14D22
zbMATH DE Number: 6077520
zbMATH Keywords: rationally connected varieties
zbMATH Keywords: weak approximation
zbMATH Keywords: del Pezzo surfaces
MaRDI profile type: Publication
arXiv ID: 1008.2711
arXiv classification: math.AG
Recommended article: Weak approximation over function fields of curves over large or finite fields
Recommended article: Q4668442
Recommended article: Weak approximation over function fields
Recommended article: Approximation faible aux places de bonne réduction sur les surfaces cubiques sur les corps de fonctions
Recommended article: Approximation faible pour les 0-cycles sur un produit de variétés rationnellement connexes
Recommended article: Q2770272
Recommended article: Rational points of rationally simply connected varieties over global function fields
Recommended article: Approximation at places of bad reduction for rationally connected varieties
Recommended article: Weak Approximation for Tori Over p-adic Function Fields
Recommended article: Q3752466
title: Weak approximation and rationally connected varieties over function fields of curves
review text: This is a survey about weak approximations for rationally connected varieties over the function field of a complex curve.NEWLINENEWLINEThe author discusses general properties of weak approximation over function fields of a curve, and proves some partial results supporting his conjecture (with Y. Tschinkel) that weak approximation always holds for rationally connected varieties over the function field of a curve.NEWLINENEWLINEAmong the results proved in the survey are the followings: weak approximation at places of good reduction, for low degree hypersurfaces (at all places) and rationally simply connected varieties (at all places).NEWLINENEWLINEIn the appendix, the author discusses some properties of stable maps used in the proof.NEWLINENEWLINEFor the entire collection see [Zbl 1237.14006].
reviewed by: Zhiyu Tian
description: scientific article; zbMATH DE number 6077520