2
$\begingroup$

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?

$\endgroup$
5
$\begingroup$

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.

| cite | improve this answer | |
$\endgroup$
  • 4
    $\begingroup$ 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
  • 2
    $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy