Rigid curves on \(\overline M_{0,n}\) and arithmetic breaks
type: Item
instance of: scholarly article
zbMATH Open document ID: 1254.14028
author: Ana-Maria Castravet
author: Jenia Tevelev
publication date: 2012-07-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/1109.6705
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14M99
Mathematics Subject Classification ID: 14G40
zbMATH DE Number: 6052323
zbMATH Keywords: moduli space of pointed curves of genus zero
zbMATH Keywords: F-conjecture
zbMATH Keywords: F-curves
zbMATH Keywords: rigid curves
MaRDI profile type: Publication
arXiv ID: 1109.6705
arXiv classification: math.AG
title: Rigid curves on \(\overline M_{0,n}\) and arithmetic breaks
review text: The authors of the article construct rigid curves on \(\overline{M}_{0,n}\) that intersect the interior \(M_{0,n}\). The main motivation is that by a Theorem of \textit{S. Keel} and \textit{J. McKernan} [``Contractible Extremal Rays on \(\overline{M}_{0,n}\)'', \url{arXiv:alg-geom/9607009}] every hypothetical counterexample to the \(F\)-conjecture is a curve as above. The main idea, used in finding such curves, is that if a curve is an irreducible component of the exceptional set of a birational morphism, then it is rigid. The authors consider birational morphisms given by hypergraph constructions, special types of forgetful morphisms. These morphisms however have usually higher dimensional exceptional components. It is shown in the article that for one special case, given by the Hesse configuration, one can find a one dimensional irreducible component, and hence a rigid curve. It is also shown that unfortunately the found rigid curve does not give counterexample to the \(F\)-conjecture. That is, the found rigid curve is decomposed into a sum of \(F\)-curves using reduction mod \(p\).NEWLINENEWLINEFor the entire collection see [Zbl 1236.14001].
reviewed by: Zsolt Patakfalvi
description: scientific article; zbMATH DE number 6052323