An explicit expression of the L\"uroth invariant

Romain Basson (1) , Reynald Lercier (1) , Christophe Ritzenthaler (2) , Jeroen Sijsling (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IML - Institut de mathématiques de Luminy

In this note, we give an algorithm to get an explicit expression of the Lüroth invariant in terms of the Dixmier-Ohno invariants. We also get the explicit factorized expression on the locus of Ciani quartics in terms of the coefficients. Finally, we answer two open questions on sub-loci of singular Lüroth quartics.

Mots clés: Dixmier-Ohno invariants; Ciani quartic; algorithm; invariant; genus 3; Dixmier-Ohno invariants.; ternary quartic

Domaines: Géométrie algébrique [math.AG]

Romain Basson, Reynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling. An explicit expression of the L\"uroth invariant. ISSAC'13, Jun 2013, Boston, United States. pp.31-36, ⟨10.1145/2465506.2465507⟩. ⟨hal-00770173⟩