2009/03/30 by Giorgio Ottaviani, Ottaviani, Giorgio, Edoardo Sernesi +1 · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #math.AG #msc:14D20 #msc:14H45 #msc:14J26 #msc:15A72
paper · pdf · doi:10.48550/arxiv.0903.5149
Final version to appear in Michigan Math. Journal. The last section of v1 has been removed and expanded in the paper "On singular Luroth quartics", arXiv:0911.2101v1
arxiv created 2009/11/11 · arxiv updated 2009/12/01
The hypersurface of Luroth quartic curves inside the projective space of plane quartics has degree 54. We give a proof of this fact along the lines outlined in a paper by Morley, published in 1919. Another proof has been given by Le Potier and Tikhomirov in 2001, in the setting of moduli spaces of vector bundles on the projective plane. Morley's proof uses the description of plane quartics as branch curves of Geiser involutions and gives new geometrical interpretations of the 36 planes associated to the Cremona hexahedral representations of a nonsingular cubic surface.