THE LOCUS OF SMOOTH PLANE CURVES WITH A SEXTACTIC POINT

Abstract

Let Mg be the moduli space of isomorphism classes of genus g smooth curves over ℂ. We show that the locus S2d-r ⊂ Mg whose general points represent smooth plane curves of degree d ≥ 4 with a sextactic point of sextactic order 2d - r, where r ∈ {0, 1, 2}, is an irreducible and rational subvariety of codimension d(d - 4) + 2 - r of Mg. These results generalize those results introduced by the author in case of quartic curves (see K. Alwaleed and M. Farahat, The locus of smooth quartic curves with a sextactic point, Appl. Math. Inf. Sci.7(2) (2013) 509–513).