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Degree of strata of singular cubic surfaces
Authors:Rafael Herná  ndez   Marí  a J. Vá  zquez-Gallo
Affiliation:Departamento de Matematicas, Facultad de Ciencias, Universidad Autonoma de Madrid, Madrid, 28049, Spain ; Departamento de Matematicas, Facultad de Ciencias, Universidad Autonoma de Madrid, Madrid, 28049, Spain
Abstract:

We determine the degree of some strata of singular cubic surfaces in the projective space $mathbf{P}^3$. These strata are subvarieties of the $mathbf{P}^{19}$ parametrizing all cubic surfaces in $mathbf{P}^3$. It is known what their dimension is and that they are irreducible. In 1986, D. F. Coray and I. Vainsencher computed the degree of the 4 strata consisting on cubic surfaces with a double line. To work out the case of isolated singularities we relate the problem with (stationary) multiple-point theory.

Keywords:Enumerative geometry   strata of singular cubic surfaces   stationary multiple-point theory
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