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?


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.

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    $\begingroup$ 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. $\endgroup$ – Sasha Aug 25 '10 at 8:10
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    $\begingroup$ I just want to emphasize that there are many "canonical" ways to choose the centers. $\endgroup$ – Karl Schwede Aug 25 '10 at 16:58
  • $\begingroup$ and that effective can still mean a lot of iterations logic.pdmi.ras.ru/~grigorev/pub/hiron-complex_journal.pdf $\endgroup$ – O.R. Jun 3 '11 at 0:59

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