Commentarii Mathematici Helvetici

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Volume 79, Issue 3, 2004, pp. 582–604
DOI: 10.1007/s00014-004-0808-y

Published online: 2004-09-30

Combinatorics of rational singularities

Lê Dũng Tráng[1] and Meral Tosun[2]

(1) Université de Provence, Marseille, France
(2) U.N.A.M., Cuernavaca, Mexico

A normal surface singularity is rational if and only if the dual intersection graph of a desingularization satisfies some combinatorial properties. In fact, the graphs defined in this way are trees. In this paper we give geometric features of these trees. In particular, we prove that the number of vertices of valency greater than 3 in the dual intersection tree of the minimal desingularization of a rational singularity of multiplicity m greater than 3 is at most m - 2.

Keywords: classification of rational singularities, topology of singularities, dual graph, glueing of rational trees

Dũng Tráng Lê, Tosun Meral: Combinatorics of rational singularities. Comment. Math. Helv. 79 (2004), 582-604. doi: 10.1007/s00014-004-0808-y