Resolution of Singularities

Details Resolution of Singularities Resolution of Singularities

1997-09-25

arxiv.org/abs/alg-geom/9709028v1

Mathematics

Algebraic Geometry

45 pages, 7 Postscript figures, LATEX. To appear in Current Developments in Several Complex Variables, MSRI Proceedings, ed. M

Scientific paper

This article is an exposition of an elementary constructive proof of canonical resolution of singularities in characteristic zero, presented in detail in Invent. Math. 128 (1997), 207-302. We define a new local invariant and get an algorithm for canonical desingularization by successively blowing up its maximum loci. The invariant can be described by local computations that provide equations for the centres of blowing up. We describe the origin of our approach and present the proof (in the hypersurface case) in parallel with a worked example.

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