An explicit expression of the Luroth invariant

Abstract

In this short note, we give an algorithm to get an explicit expression of the Luroth 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 Luroth quartics.

References in corpus (1)

• On the rationality of the moduli space of Lüroth quartics

Cited by in corpus (2)

• Learning Algebraic Varieties from Samples
• The 3 x 3 x 3 hyperdeterminant as a polynomial in the fundamental invariants for SL(3,C) x SL(3,C) x SL(3,C)