An explicit expression of the Luroth invariant
  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. 
Romain Basson, Reynald Lercier, Christophe Ritzenthaler, Jeroen   Sijsling
math.AG