Skip to main content

Deformation and stratification of secant structure

  • 720 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 687)

Keywords

  • Secant Scheme
  • Base Extension
  • Projective Scheme
  • Closed Subscheme
  • Canonical Morphism

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Grothendieck, A., (with the collaboration of Dieudonné, J.) Elements de géométrie algébrique. Chapters I–IV. Institut des Hautes Études Scientifiques, Publ. Math. 4, 8, 11, 17, 20, 24, 28, 32. Paris 1960–1967.

    Google Scholar 

  2. Fulton, W., Rational equivalence on singular varities. Institut des Hautes Études Scientifiques, Publ. Math., 45 (1975), 147–167.

    CrossRef  MathSciNet  Google Scholar 

  3. Fulton, W., and MacPherson, R., Intersecting cycles on an algebraic variety. Preprint Series 1976/77, No. 14, Department of Mathematics, Aarhus Univ.

    Google Scholar 

  4. Holme, A., The notion of secant scheme for quasi-projective morphisms. Seminar reports, Matematisk Seminar, Univ. of Oslo, (1969).

    Google Scholar 

  5. _____, Formal embedding and projection theorems. Amer. Journ. of Math., 93 (1971), 527–571.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. _____, A general embedding theorem in formal geometry. Compositio Math., 26 (1973), 41–68.

    MathSciNet  MATH  Google Scholar 

  7. _____, Projections of non-singular projective varieties. J. Math. Kyoto Univ. 13 (1973), 301–322.

    MathSciNet  MATH  Google Scholar 

  8. _____, An embedding-obstruction for algebraic varieties. Bull. Amer. Math Soc. 80 (1974), 932–934.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. _____, Embedding obstruction for smooth, projective varieties I. To appear in Advances in Mathematics (1977), Preprint Series, Univ. of Bergen (1974).

    Google Scholar 

  10. _____, Embedding-obstruction for singular algebraic varieties in ℙN. Acta Math. 135 (1975), 155–185.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. _____, and Roberts, J., Pinch-points and multiple locus of generic projections of singular varieties. Preprint Series, Univ. of Bergen (1976).

    Google Scholar 

  12. Johnson, K.W., Immersion and embedding of projective varieties. Thesis, Brown University, 1976.

    Google Scholar 

  13. ________, The enumerative theory of singularities. Summer School on singularities, Oslo 1976. To appear on Wolters-Noordhoff Publishing, Groningen.

    Google Scholar 

  14. Laksov, D., Some enumerative properties of secants to nonsingular schemes. Math. Scand., 39 (1976), 171–190.

    MathSciNet  MATH  Google Scholar 

  15. _____, Secant bundles and Todd's formula for the double points of maps into ℙn. Preprint.

    Google Scholar 

  16. _____, Residual intersections and Todd's formula for the double locus of a morphism. Preprint.

    Google Scholar 

  17. Laudal, O.A., Sections of functors and the problem of lifting (deforming) algebraic structures I, II, III. Preprint series, Institute of Mathematics, Univ. of Oslo (1975).

    Google Scholar 

  18. Lluis, E., Sur l'immersion des variétés algébriques, Ann. of Math., 62 (1955), 120–127.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. _____, De las singularidades que aparecen al proyectar variedades algebraicas. Bol. soc. Mat. Mexicana, 1 (1956), 1–9.

    MathSciNet  Google Scholar 

  20. _____, Variedades algebraicas con ciertas condiciones en sus tangentes. Bol. Soc. Mat. Mexicana, (1962), 47–56.

    Google Scholar 

  21. Manin, Yu.I., Lectures on the K-functor in algebraic geometry. Russian Mathematical Surveys, Vol. 24 (1969), 1–89.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. Peters, C.A.M., and Simonis, J., A secant formula. Quart. J. Math. Oxford, 27 (1976), 181–189.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. Roberts, J., The variation of singular cycles in an algebraic family of morphisms, Trans. Amer. Math. Soc. 168 (1972), 153–164.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. _____, Singularity subschemes and generic projections. Trans. Amer. Math. Soc., 212 (1975), 229–268.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. _____, A stratification of the dual variety (Summary of results with indications of proof), preprint (1976).

    Google Scholar 

  26. _____, Hypersurfaces with nonsingular normalization. Preprint (1977).

    Google Scholar 

  27. Serre, J.-P., Algèbre Locale. Multiplicités. Springer Lecture Notes, Vol. 11 (1965).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1978 Springer-Verlag

About this paper

Cite this paper

Holme, A. (1978). Deformation and stratification of secant structure. In: Olson, L.D. (eds) Algebraic Geometry. Lecture Notes in Mathematics, vol 687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062928

Download citation

  • DOI: https://doi.org/10.1007/BFb0062928

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08954-4

  • Online ISBN: 978-3-540-35688-2

  • eBook Packages: Springer Book Archive