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Suppose I have a singular projective variety defined by some homogeneous equations in complex projective space. Is the resolution of singularities effective? That is, do I actually know which smooth centers to blow up?

flag	asked Aug 25 2010 at 7:49 Colin Tan 4,191●13●43

Remke Kloosterman · Accepted Answer · 2010-08-25 07:55:37Z UTC

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Yes, in the sense that resolution of singularities is implemented in the computer algebra package Singular. See the manual of Singular for references. (There might be other/better references.) However, if I remember correctly the centers are not unique.

answered Aug 25 2010 at 7:55

Remke Kloosterman
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There are ways to choose the centers canonically. This is called "canonical resolution of singularities", see e.g. Bierstone, Edward; Milman, Pierre D. (1997), "Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant.", Invent. Math. 128 (2): 207–302. – Sasha Aug 25 2010 at 8:10

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I just want to emphasize that there are many "canonical" ways to choose the centers. – Karl Schwede Aug 25 2010 at 16:58

and that effective can still mean a lot of iterations logic.pdmi.ras.ru/~grigorev/pub/… – Franklin Jun 3 2011 at 0:59

Is resolution of singularities effective?

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