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A new characterization of rational surface singularities

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References

  1. Artin, M.: On isolated rational singularities of surfaces. Am. J. Math.88, 129–136 (1966)

    Google Scholar 

  2. Badescu, L.: Applications of the Grothendieck duality theory to the study of normal isolated singularities. Rev. Roam. Math. Pur. Appl.26 (5), 673–689 (1979)

    Google Scholar 

  3. Beltrametti, M., Sommese, A.: A criterion for a variety to be a cone. Comm. Math. Helv.62, 417–422 (1987)

    Google Scholar 

  4. Cutkosky, S.: Factorization of complete ideals. J. Alg.115, 144–149 (1988)

    Google Scholar 

  5. Cutkosky, S.: On unique and almost unique factorization of complete ideals. Am. J. Math.111, 417–433 (1989)

    Google Scholar 

  6. Cutkosky, S.: On unique and almost unique factorization of complete ideals II. Invent. Math.98, 59–74 (1989)

    Google Scholar 

  7. Gohner, H.: Semi-factoriality and Muhly's condition (N) in two dimensional local rings. J. Alg.34, 403–429 (1975)

    Google Scholar 

  8. Hartshorne, R.: Algebraic geometry. Berlin, Heidelberg, New York: Springer 1977

    Google Scholar 

  9. Huneke, C., Sally, J.: Birational extensions in dimension two and integrally closed ideals. J. Alg.115, 481–500 (1988)

    Google Scholar 

  10. Kawamata, Y, Matsuda, K., Matsuki, K.: Introduction to the minimal model problem. In: Oda, T. (ed.), Alg. Geom. Sendai. Advanced Studies in Pure Mathematics Vol. 10, pp. 283–360. Kinokuniya-North Holland, 1987

  11. Lipman, J.: Rational singularities, with applications to algebraic surfaces and unique factorization. Publ. Math. Inst. Hautes Etudes Sci.36 (1969)

  12. Muhly, H., Sakuma, M.: Asymptotic factorization of ideals. J. London Math. Soc.38 341–350 (1963)

    Google Scholar 

  13. Reid, M.: Canonical threefolds. Journees de Geometrie algebrique d'Angers. pp. 273–310. Sitjhoff and Nordhoff 1980

  14. Weil, A.: Basic number theory. Berlin, Heidelberg, New York: Springer 1967

    Google Scholar 

  15. Zariski, O.: Polynomial ideals defined by infinitely near base points. Am. J. Math.60, 151–204 (1938)

    Google Scholar 

  16. Zariski, O.: Theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface. Ann. Math.76, 560–615 (1962)

    Google Scholar 

  17. Zariski, O., Samuel, P.: Commutative Algebra. Vol. 2. Princeton: Van Nostrand 1960

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri-Columbia, 65211, Columbia, MO, USA

    Steven Dale Cutkosky

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  1. Steven Dale Cutkosky
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Oblatum 29-IX-1989 & 29-I-1990

Partially supported by NSF

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Cutkosky, S.D. A new characterization of rational surface singularities. Invent Math 102, 157–177 (1990). https://doi.org/10.1007/BF01233425

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