McMullen, Curtis T.; Mukamel, Ronen E.; Wright, Alex Cubic curves and totally geodesic subvarieties of moduli space. (English) Zbl 1460.14062 Ann. Math. (2) 185, No. 3, 957-990 (2017). 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. Reviewer: Dawei Chen (Chestnut Hill) Cited in 3 ReviewsCited in 28 Documents MSC: 14H10 Families, moduli of curves (algebraic) 32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) Keywords:Hodge theory; Teichmüller theory; dynamics on moduli spaces; elliptic curves PDFBibTeX XMLCite \textit{C. T. McMullen} et al., Ann. Math. (2) 185, No. 3, 957--990 (2017; Zbl 1460.14062) Full Text: DOI Link