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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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  • 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