Explicit Resolutions of Double Point Singularities of Surfaces

Details Explicit Resolutions of Double Point Singularities of Surfaces Explicit Resolutions of Double Point Singularities of Surfaces

1999-11-23

arxiv.org/abs/math/9911183v3

Mathematics

Algebraic Geometry

31 pages; partially rewritten

Scientific paper

Locally analytically, any isolated double point occurs as a double covering of a smooth surface. It can be desingularized via the canonical resolution, as it is well-known. In this paper we explicitly compute the fundamental cycle of both the canonical and minimal resolution of a double point singularity and we classify those for which the fundamental cycle differs from the fiber cycle. Finally we compute the conditions that a double point imposes to pluricanonical systems.

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