Rationality of moduli spaces of plane curves of small degree

2008/04/09 by Christian Böhning, Hans-Christian Graf v. Bothmer, Hans-Christian Graf von Bothmer +1 · 1 voice
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #math.AG #msc:14E08 #msc:14L24 #msc:14M20

paper · pdf · doi:10.1007/s00222-009-0214-6

published as Exp. Math. 18, No. 4, 499-508 (2009). · 17 pages

arxiv created 2009/04/06 · openalex publication_date 2009/08/18 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that the moduli space C(d) of plane curves of degree d (for projective equivalence) is rational except possibly if d= 6, 7, 8, 11, 12, 14, 15, 16, 18, 20, 23, 24, 26, 32, 48.

Discussions

• I seem to understand that the moduli space of plane sextic (say, the GIT quotient w.r.t. $PGL(3)$ ) is not known yet to be rational. It is excluded from the list given here https://link.springer.com/a [stackexchange, 2 points]