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)

 
 

 

Embeddings in $ G(1,\,3)$


Author: A. Papantonopoulou
Journal: Proc. Amer. Math. Soc. 89 (1983), 583-586
MSC: Primary 14J25; Secondary 14E25, 14M15
DOI: https://doi.org/10.1090/S0002-9939-1983-0718977-3
Corrigendum: Proc. Amer. Math. Soc. 95 (1985), 533-536.
MathSciNet review: 718977
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give a description of nonsingular surfaces of degree $ d \leqslant 8$ in the Grassmannian $ G(1,3)$ embedded in $ {{\mathbf{P}}^5}$.


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

  • [1] A. Beauville, Surfaces algébriques complexes, Astérisque 54 (1978). MR 0485887 (58:5686)
  • [2] E. Bomberi and D. Husemoller, Classification and embeddings of surfaces, Proc. Symp. Pure Math., vol. 29, Amer. Math. Soc., Providence, R.I., 1975, pp. 329-420. MR 0506292 (58:22085)
  • [3] L. Ein, Nondegenerate surfaces of degree $ n + 3$ in $ P_C^n$, preprint.
  • [4] R. Hartshorne, Curves with high self-intersection on algebraic surfaces, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 111-125. MR 0266924 (42:1826)
  • [5] -, Algebraic geometry, Graduate Texts in Math., no. 52, Springer-Verlag, New York and Heidelberg, 1977. MR 0463157 (57:3116)
  • [6] K. Kulek, The normal bundle of a curve on a quadric, Math. Ann. 258 (1981), 201-206. MR 641825 (83e:14034)
  • [7] D. Mumford, Abelian varieties, Oxford Univ. Press, New York and London, 1970. MR 0282985 (44:219)
  • [8] M. Nagata, On rational surfaces. I, Mem. Colloq. Sci. Kyoto Ser. A 32 (1960), 351-370. MR 0126443 (23:A3739)
  • [9] A. Papantonopoulou, Curves in Grassmann varieties, Nagoya Math. J. 66 (1977), 121-137. MR 0437551 (55:10475)
  • [10] L. Roth, On surfaces of sectional genus four, Proc. Cambridge Philos. Soc. 29 (1933), 184-194.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14J25, 14E25, 14M15

Retrieve articles in all journals with MSC: 14J25, 14E25, 14M15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0718977-3
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society