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Degree of strata of singular cubic surfaces |
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| 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 |
| Keywords: | Enumerative geometry strata of singular cubic surfaces stationary multiple-point theory |
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. These strata are subvarieties of the 
parametrizing all cubic surfaces in 
. 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.