Degree of strata of singular cubic surfaces
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- by Rafael Hernández and María J. Vázquez-Gallo PDF
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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.References
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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
- Received by editor(s): March 15, 1999
- Published electronically: August 9, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 95-115
- MSC (2000): Primary 14N05, 14C17; Secondary 14C05, 14C15
- DOI: https://doi.org/10.1090/S0002-9947-00-02585-X
- MathSciNet review: 1707194