2009/11/11 by Giorgio Ottaviani, Ottaviani, Giorgio, Edoardo Sernesi +1
Computer Science · Mathematics · #14D20 #14H45 #14J26 #15A72 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14D20 #msc:14H45 #msc:14J26 #msc:15A72
paper · pdf · doi:10.48550/arxiv.0911.2101
Enlarged version. Computation of the class of the locus of Luroth quartics in the moduli space added
openalex publication_date 2009/11/11 · arxiv created 2010/07/09 · arxiv updated 2010/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Plane quartics containing the ten vertices of a complete pentalateral and limits of them are called Lüroth quartics. The locus of singular Lüroth quartics has two irreducible components, both of codimension two in ¶14. We compute the degree of them and we discuss the consequences of this computation on the explicit form of the Lüroth invariant. One important tool are the Cremona hexahedral equations of the cubic surface. We also compute the class in M3 of the closure of the locus of nonsingular Lüroth quartics.