On isolated singularities of surfaces which do not affect the conditions of adjunction (Part I.)

Patrick Du Val

doi:10.1017/S030500410001269X

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Cited by 29
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Roth, L. 1952. Some threefolds on which adjunction terminates. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 48, Issue. 02, p. 233.

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Herszberg, J. and Rees, D. 1962. On certain types of isolated s-ple points on algebraic primals in Sd. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 58, Issue. 03, p. 465.

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Val, Patrick du 1967. Rational Surfaces with Exceptional Unodes. Canadian Journal of Mathematics, Vol. 19, Issue. , p. 938.

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1986. Cubic Forms - Algebra, Geometry, Arithmetic. Vol. 4, Issue. , p. 284.

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Volume 30, Issue 4
October 1934 , pp. 453-459

On isolated singularities of surfaces which do not affect the conditions of adjunction (Part I.)

Patrick Du Val ^(a1)

- DOI: https://doi.org/10.1017/S030500410001269X
- Published online by Cambridge University Press: 24 October 2008

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By an isolated singularity of an algebraic surface in [r] (i.e. space of r dimensions) I shall mean one which not merely is not upon any branch of a multiple curve of the surface, but has also the property that when the surface is projected into [3] from a general space [r − 4] the singular point remains in isolation, i.e. no branch of the double curve created by the projection will of necessity pass through it.

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† Enriques, F. and Campedella, L., Lezioni sulla teoria delle superficie algebriche, § 39.

† Actually, Coxeter uses N ₀, …, N _n−1, etc., but the alteration introduced here seems to make for convenience.

‡ Salmon, , Analytical geometry of three dimensions, vol. 2 (1915), art. 522.

† Klein, Felix, Gesammelte mathematische Abhandlungen, 2, p. 11 = Math. Ann. 6 (1873), 551.

‡ Enriques and Campedella, op. cit. § 59.

† Enriques and Campedella, op. cit. § 60.

† Coxeter, H. S. M., “The polytopes with regular prismatic vertex figures, Part 2,” Proc. Lond. Math. Soc. (2), 34 (1932), 126–189 (135–151).

‡ See Coxeter, loc. cit. p. 137.

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Cited by 29
Cited by
- 29
Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

Roth, L. 1952. Some threefolds on which adjunction terminates. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 48, Issue. 02, p. 233.

CrossRef

Google Scholar

Herszberg, J. and Rees, D. 1962. On certain types of isolated s-ple points on algebraic primals in Sd. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 58, Issue. 03, p. 465.

CrossRef

Google Scholar

Val, Patrick du 1967. Rational Surfaces with Exceptional Unodes. Canadian Journal of Mathematics, Vol. 19, Issue. , p. 938.

CrossRef

Google Scholar

Lipman, Joseph 1969. Rational singularities, with applications to algebraic surfaces and unique factorization. Publications mathématiques de l'IHÉS, Vol. 36, Issue. 1, p. 195.

CrossRef

Google Scholar

Yau, Stephen S. T. 1977. Two theorems on higher dimensional singularities. Mathematische Annalen, Vol. 231, Issue. 1, p. 55.

CrossRef

Google Scholar

Pinkham, H. 1980. Séminaire sur les Singularités des Surfaces. Vol. 777, Issue. , p. 10.

CrossRef

Google Scholar

Pinkham, H. 1980. Séminaire sur les Singularités des Surfaces. Vol. 777, Issue. , p. 147.

CrossRef

Google Scholar

Brenton, Lawrence 1980. On singular complex surfaces with negative canonical bundle, with applications to singular compactifications ofC 2 and to 3-dimensional rational singularities. Mathematische Annalen, Vol. 248, Issue. 2, p. 117.

CrossRef

Google Scholar

Teissier, B. 1980. Séminaire sur les Singularités des Surfaces. Vol. 777, Issue. , p. 82.

CrossRef

Google Scholar

Kumar, N. Mohan 1981. Rational double points on a rational surface. Inventiones Mathematicae, Vol. 65, Issue. 2, p. 251.

CrossRef

Google Scholar

1986. Cubic Forms - Algebra, Geometry, Arithmetic. Vol. 4, Issue. , p. 284.

CrossRef

Google Scholar

Persson, Ulf 1990. Configurations of Kodaira fibers on rational elliptic surfaces. Mathematische Zeitschrift, Vol. 205, Issue. 1, p. 1.

CrossRef

Google Scholar

Miranda, Rick 1990. Persson's list of singular fibers for a rational elliptic surface. Mathematische Zeitschrift, Vol. 205, Issue. 1, p. 191.

CrossRef

Google Scholar

Wall, C.T.C. 1990. Deformations of real singularities. Topology, Vol. 29, Issue. 4, p. 441.

CrossRef

Google Scholar

Yamada, Hiroshi 1995. Lie group theoretical construction of period mapping. Mathematische Zeitschrift, Vol. 220, Issue. 1, p. 231.

CrossRef

Google Scholar

Dais, Dimitrios I. Haus, Utz-Uwe and Henk, Martin 1998. On crepant resolutions of 2-parameter series of Gorenstein cyclic quotient singularities. Results in Mathematics, Vol. 33, Issue. 3-4, p. 208.

CrossRef

Google Scholar

Barrow-Green, June and Gray, Jeremy 2006. Geometry at Cambridge, 1863–1940. Historia Mathematica, Vol. 33, Issue. 3, p. 315.

CrossRef

Google Scholar

Kapustka, Grzegorz and Kapustka, Michał 2009. Equations of log del Pezzo surfaces of index ≤ 2. Mathematische Zeitschrift, Vol. 261, Issue. 1, p. 169.

CrossRef

Google Scholar

Brav, Christopher and Thomas, Hugh 2011. Braid groups and Kleinian singularities. Mathematische Annalen, Vol. 351, Issue. 4, p. 1005.

CrossRef

Google Scholar

Friedmann, Tamar 2011. Orbifold singularities, Lie algebras of the third kind (LATKes), and pure Yang–Mills with matter. Journal of Mathematical Physics, Vol. 52, Issue. 2, p. 022304.

CrossRef

Google Scholar

Download full list

Google Scholar Citations

View all Google Scholar citations for this article.

Scopus Citations

View all citations for this article on Scopus

Volume 30, Issue 4
October 1934 , pp. 453-459

On isolated singularities of surfaces which do not affect the conditions of adjunction (Part I.)

Patrick Du Val ^(a1)

- DOI: https://doi.org/10.1017/S030500410001269X
- Published online by Cambridge University Press: 24 October 2008

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On isolated singularities of surfaces which do not affect the conditions of adjunction (Part I.)

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