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arXiv · 0804.4062

On the exceptional locus of the birational projections of normal surface singularity into a plane

Jesus Fernandez-Sanchez
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Abstract

Given a normal surface singularity $(X, Q)$ and a birational morphism to a non- singular surface $π: X \to S$, we investigate the local geometry of the exceptional divisor $L$ of $π$. We prove that the dimension of the tangent space to $L$ at $Q$ equals the number of exceptional components meeting at $Q$. Consequences relative to the existence of such birational projections contracting a prescribed number of irreducible curves are deduced. A new characterization of minimal singularities is obtained in these terms.

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Jesus Fernandez-Sanchez. 2008-04-25. On the exceptional locus of the birational projections of normal surface singularity into a plane. https://arxiv.org/abs/0804.4062

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