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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Degree of strata of singular cubic surfaces


Authors: Rafael Hernández and María J. Vázquez-Gallo
Journal: Trans. Amer. Math. Soc. 353 (2001), 95-115
MSC (2000): Primary 14N05, 14C17; Secondary 14C05, 14C15
Published electronically: 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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Additional Information

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: http://dx.doi.org/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
Published electronically: August 9, 2000
Article copyright: © Copyright 2000 American Mathematical Society