Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Every curve on a nonsingular surface can be defined by two equations

Author: M. Boratyński
Journal: Proc. Amer. Math. Soc. 96 (1986), 391-393
MSC: Primary 14M10; Secondary 14C10
MathSciNet review: 822425
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ R$ be a smooth two-dimensional affine algebra over an algebraically closed field, and let $ I$ be an unmixed ideal of height one in $ R$. Then there exist $ a,b$ in $ I$ such that $ {\text{rad}}(I) = {\text{rad}}(a,b)$.

References [Enhancements On Off] (What's this?)

  • [1] L. Claborn and R. Fossum, Generalization of the notion of class group, Illinois J. Math. 12 (1968), 228-253. MR 0224601 (37:200)
  • [2] W. Fulton, Rational equivalence on singular varieties, Inst. Hautes Études Sci. Publ. Math. 45 (1975), 147-167. MR 0404257 (53:8060)
  • [3] A. Grothendieck, La théorie des classes de Chern, Bull. Soc. Math. France 86 (1958), 137-154. MR 0116023 (22:6818)
  • [4] M. P. Murthy and R. G. Swan, Vector bundles over affine surfaces, Invent. Math. 36 (1976), 125-165. MR 0439842 (55:12724)
  • [5] J. P. Serre, Sur les modules projectives, Sem. Dubreil-Pisot, 1960/1961.
  • [6] B. L. van der Waerden, Review, Zbl. Math. 24 (1941), 276.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14M10, 14C10

Retrieve articles in all journals with MSC: 14M10, 14C10

Additional Information

Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society