Degree of strata of singular cubic surfaces

Hernández, Rafael; Vázquez-Gallo, María

doi:10.1090/S0002-9947-00-02585-X

Degree of strata of singular cubic surfaces
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by Rafael Hernández and María J. Vázquez-Gallo PDF

Trans. Amer. Math. Soc. 353 (2001), 95-115 Request permission

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.

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