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Mathematics > Algebraic Geometry

arXiv:0707.1387 (math)
[Submitted on 10 Jul 2007]

Title:Equisingularity classes of birational projections of normal singularities to a plane

Authors:Maria Alberich-Carraminana, Jesus Fernandez-Sanchez
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Abstract: Given a birational normal extension S of a two-dimensional local regular ring R, we describe all the equisingularity types of the complete ideals J in R whose blowing-up has some point at which the local ring is analytically isomorphic to S.
The problem of classifying the germs of such normal surface singularities was already posed by Spivakovsky (Ann. of Math. 1990). This problem has two parts: discrete and continous. The continous part is to some extent equivalent to the problem of the moduli of plane curve singularities, while the main result of this paper solves completely the discrete part.
Comments: 22 pages, 3 figures. To appear in Advances in Mathematics
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC)
MSC classes: 14B05; 32S05; 13B22
Cite as: arXiv:0707.1387 [math.AG]
  (or arXiv:0707.1387v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.0707.1387

Submission history

From: Jesus Fernandez [view email]
[v1] Tue, 10 Jul 2007 11:47:53 UTC (101 KB)
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