Israel Journal of Mathematics

, Volume 204, Issue 1, pp 97–143 | Cite as

Embedded Q-resolutions for Yomdin-Lê surface singularities



In a previous work we have introduced and studied a special kind of toric resolution, the so-called embedded Q-resolution, which essentially consists in allowing the final ambient space to contain abelian quotient singularities. Here we explicitly compute an embedded Q-resolution of a Yomdin-Lê surface singularity (V, 0) in terms of a (global) embedded Q-resolution of its tangent cone by means of just weighted blow-ups at points. The generalized A’Campo’s formula in this setting is applied so as to compute the characteristic polynomial. As a consequence, an exceptional divisor in the resolution of (V, 0), apart from the first one which might be special, contributes to its complex monodromy if and only if so does the corresponding divisor in the tangent cone. Thus the resolution obtained is optimal in the sense that the weights can be chosen so that every exceptional divisor in the Q-resolution of (V, 0), except perhaps the first one, contributes to its monodromy.


Characteristic Polynomial Euler Characteristic Quotient Space Ambient Space Tangent Cone 
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© Hebrew University of Jerusalem 2014

Authors and Affiliations

  1. 1.Academia General MilitarCentro Universitario de la Defensa - IUMAZaragozaSpain

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