Timeline for Is there an upper bound and a lower bound on the contribution to the genus, for a singularity of codimension k?
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| Oct 15, 2011 at 6:56 | comment | added | quim | Yes. Their formula counts the number of conditions imposed by the singularity in a fixed position of the points of the resolution, and then subtracts the degrees of freedom for the positions of these points, resulting in the codimension you refer to. Maybe you'd find interesting their more recent work, arXiv:0905.2169, appeared I think in Rendiconti Lincei. | |
| Oct 14, 2011 at 22:27 | comment | added | Ritwik | Thank you for the reference. I need to be sure of something. Is codimension, intuitively the ``number of conditions'' needed to specify the singularity? For instance I would say a tacnode (A_3) is codimension 3 because you need 3 conditions to specify a tacnode. From their defenition of codimension on Page 214, it doesn't seem to be immediately obvious. | |
| Oct 14, 2011 at 9:58 | history | edited | quim | CC BY-SA 3.0 |
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| Oct 14, 2011 at 8:57 | comment | added | quim | I modified the answer to deal with your comments, hope it is clearer now. | |
| Oct 14, 2011 at 8:56 | history | edited | quim | CC BY-SA 3.0 |
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| Oct 14, 2011 at 0:46 | vote | accept | Ritwik | ||
| Oct 14, 2011 at 0:36 | comment | added | Ritwik | I am sorry, the lower bound can not possibly follow from that equation! | |
| Oct 13, 2011 at 22:43 | comment | added | Ritwik | Thank you for your answer. Is there any reference you can point out to me where I will get this result? And I assume you are saying both my bounds follow? The upper bound and the lower bound? | |
| Oct 13, 2011 at 21:02 | history | answered | quim | CC BY-SA 3.0 |