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