Transactions of the American Mathematical Society

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
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14N05, 14C17, 14C05, 14C15

Rafael Hernández
Affiliation: Departamento de Matematicas, Facultad de Ciencias, Universidad Autonoma de Madrid, Madrid, 28049, Spain
Email: rafael.hernandez@uam.es

María J. Vázquez-Gallo
Affiliation: Departamento de Matematicas, Facultad de Ciencias, Universidad Autonoma de Madrid, Madrid, 28049, Spain
Email: mjesus.vazquez@uam.es

DOI: 10.1090/S0002-9947-00-02585-X
PII: S 0002-9947(00)02585-X
Keywords: Enumerative geometry, strata of singular cubic surfaces, stationary multiple-point theory
Received by editor(s): March 15, 1999
Posted: August 9, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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