Cubic curves and totally geodesic subvarieties of moduli space
type: Item
instance of: scholarly article
title: Cubic curves and totally geodesic subvarieties of moduli space
zbMATH Open document ID: 1460.14062
author: Curtis T. McMullen
author: Ronen E. Mukamel
author: Alex Wright
published in: Annals of Mathematics. Second Series
publication date: 2017-06-16T00:00:00Z
full work available at URL: urn-3:HUL.InstRepos:34334609
review text: The flex locus parameterizes plane cubics with three collinear cocritical points under a projection, and the gothic locus arises from quadratic differentials with zeros at a fiber of the projection and with poles at the cocritical points. In this paper the authors show that the flex locus provides the first example of a primitive totally geodesic subvariety of moduli space and the gothic locus provides new \(\mathrm{SL}_2(\mathbb R)\)-invariant varieties in Teichmüller dynamics. A number of interesting properties of these loci from the viewpoints of projective geometry and flat surfaces are discussed.
reviewed by: Dawei Chen
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 32G15
zbMATH DE Number: 6731862
zbMATH Keywords: Hodge theory
zbMATH Keywords: Teichmüller theory
zbMATH Keywords: dynamics on moduli spaces
zbMATH Keywords: elliptic curves
MaRDI profile type: Publication
OpenAlex ID: W2590037223
DOI: 10.4007/ANNALS.2017.185.3.6
description: scientific article