On singular Luroth quartics

Details On singular Luroth quartics On singular Luroth quartics

2009-11-11

arxiv.org/abs/0911.2101v2

Mathematics

Algebraic Geometry

Enlarged version. Computation of the class of the locus of Luroth quartics in the moduli space added

Scientific paper

Plane quartics containing the ten vertices of a complete pentalateral and limits of them are called L\"uroth quartics. The locus of singular L\"uroth quartics has two irreducible components, both of codimension two in $\P^{14}$. We compute the degree of them and we discuss the consequences of this computation on the explicit form of the L\"uroth invariant. One important tool are the Cremona hexahedral equations of the cubic surface. We also compute the class in $\overline{M}_3$ of the closure of the locus of nonsingular L\"uroth quartics.

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