Towards the degree of the PGL(4)-orbit of a cubic surface

  • Elisa Cazzador University of Oslo
  • Bjørn Skauli University of Oslo


We study the action of the group PGL(4) on the parameter space P 19
of complex cubic surfaces. Specifically, we look at how the techniques
used by Aluffi and Faber in [1] can be extended to compute the degree of
the orbit closure O of a general cubic surface. We study the base locus of
the induced rational map P15 ⤏ O ⊂ P19 , and the first steps in resolving
this rational map by successively blowing up the reduced base locus.