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

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

2008-04-25

arxiv.org/abs/0804.4062v1

Mathematics

Algebraic Geometry

12 pages, 2 figures

Scientific paper

Given a normal surface singularity $(X, Q)$ and a birational morphism to a non- singular surface $\pi : X \to S$, we investigate the local geometry of the exceptional divisor $L$ of $\pi$. 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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