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ISSN 1088-6850(e) ISSN 0002-9947(p)

Degree of strata of singular cubic surfaces

Author(s): Rafael Hernández; María J. Vázquez-Gallo
Journal: Trans. Amer. Math. Soc. 353 (2001), 95-115.
MSC (2000): Primary 14N05, 14C17; Secondary 14C05, 14C15
Posted: August 9, 2000
MathSciNet review: 1707194
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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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