Skip to main content
SpringerLink
Log in

Rees valuations

  • Published:
Proceedings - Mathematical Sciences Aims and scope Submit manuscript

Abstract

We study dicritical divisors and Rees valuations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abhyankar S S, On the valuations centered in a local domain, Am. J. Math. 78 (1956) 321–348

    Article  MathSciNet  MATH  Google Scholar 

  2. Abhyankar S S, Ramification Theoretic Methods in Algebraic Geometry (Princeton University Press) (1959)

  3. Abhyankar S S, Resolution of Singularities of Embedded Algebraic Surfaces, First edition of 1966 published by Academic Press, Second enlarged edition of 1998 published by Springer-Verlag

  4. Abhyankar S S, Historical ramblings in algebraic geometry and related algebra, Am. Math. Mon. 83 (1976) 409–448

    Article  MathSciNet  MATH  Google Scholar 

  5. Abhyankar S S, Desingularization of plane curves, Singularities, Proceedings of Symposia in Pure Mathematics, American Mathematical Society (1983) vol 40, Part 1, pages 1–45

  6. Abhyankar S S, Algebraic Geometry for Scientists and Engineers, Am. Math. Soc. (1990)

  7. Abhyankar S S, Polynomial expansion, Proceedings of the American Mathematical Society (1998) vol 126, pages 1583–1596

  8. Abhyankar S S, Lectures on Algebra I, (World Scientific) (2006) Journal of Algebra, (2008) vol. 319, pages 2720–2826

  9. Abhyankar S S, Inversion and Invariance of Characteristic Terms Part I, K Alladi et al (eds), The legacy of Alladi Ramakrishnan in the Mathematical Sciences, Springer (2010) pp. 93–168

  10. Abhyankar S S, Dicritical Divisors and Jacobian Problem, Indian J. Pure Appl. Math. 41 (2010) 77–97

    Article  MathSciNet  MATH  Google Scholar 

  11. Abhyankar S S, Pillars and Towers of Quadratic Transformations, Proc. Am. Math. Soc. 139 (2011) 3067–3082

    Article  MathSciNet  MATH  Google Scholar 

  12. Abhyankar S S, More about dicriticals, Proc. Am. Math. Soc. 139 (2011) 3083–3097

    Article  MathSciNet  MATH  Google Scholar 

  13. Abhyankar S S, Quadratic transforms inside their generic incarnations, Proc. Am. Math. Soc. 140 (2012)

  14. Abhyankar S S, Dicritical Divisors and Dedekind’s Gauss Lemma, Revista Mathematica Complutense (2012)

  15. Abhyankar S S and Artal Bartolo E, Algebraic theory of curvettes and dicriticals, to appear

  16. Abhyankar S S and Heinzer W J, Existence of dicritical divisors, Am. J. Math. 134 (2012) 171–192

    Article  MathSciNet  MATH  Google Scholar 

  17. Abhyankar S S and Heinzer W J, Existence of dicritical divisors revisited, Proc. Indian Acad. Sci. (Math. Sci.) 121 (2011) 267–290

    MathSciNet  Google Scholar 

  18. Abhyankar S S and Luengo I, Algebraic theory of dicritical divisors, Am. J. Math., 133 (2011) 1713–1732

    Article  MathSciNet  Google Scholar 

  19. Artal-Bartolo E, Une démonstration géométrique du théorèm d’Abhyankar-Moh, Crelle J. 464 (1995) 97–108

    MathSciNet  MATH  Google Scholar 

  20. Eisenbud D and Neumann W D, Three-dimensional link theory and invariants of plane curve singularities, Ann. Math. Stud. 101 (1985)

  21. Fourrier L, Topologie d’un polynome de deux variables complexes au voisinage de l’infini, Annales de l’institut Fourier 46 (1996) 645–687

    Article  MathSciNet  MATH  Google Scholar 

  22. Huneke C, Complete ideals in two dimensional regular local rings, Commutative Algebra, Berkeley, California 1987, Math. Sci. Res. Inst. Publ., 15 (New York: Springer) (1989)

  23. Le D T and Weber C, A geometrical approach to the Jacobian conjecture for n = 2, Kodai J. Math. 17 (1994) 375–381

    Google Scholar 

  24. Mattei J F and Moussu R, Holonomie et intégrales premières, Ann. Scient. Écoles Norm. Sup. 13 (1980) 469–523

    MathSciNet  MATH  Google Scholar 

  25. Nagata M, Local Rings (Wiley) (1962)

  26. Northcott D G and Rees D, Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954) 145–158

    Article  MathSciNet  MATH  Google Scholar 

  27. Zariski O and Samuel P, Commutative Algebra, Volumes I and II (Springer-Verlag) (1975)

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Purdue University, West Lafayette, IN, 47907, USA

    SHREERAM S ABHYANKAR & WILLIAM J HEINZER

Authors
  1. SHREERAM S ABHYANKAR
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. WILLIAM J HEINZER
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to SHREERAM S ABHYANKAR.

Rights and permissions

Reprints and permissions

About this article

Cite this article

ABHYANKAR, S.S., HEINZER, W.J. Rees valuations. Proc Math Sci 122, 525–546 (2012). https://doi.org/10.1007/s12044-012-0081-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12044-012-0081-8

Keywords

Search

Navigation