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Topic review - milnor and tjurina numbers
Author Message
renzo
  Post subject:   Reply with quote
I think it is worth mentioning that by a theorem of Saito any weighted homogeneous polynomial defining an IHS belongs to its Jacobi ideal and viceversa, therefore they have the same Turina and Milnor numbers.
Post Posted: Sat Feb 03, 2007 1:30 am
greuel
  Post subject:   Reply with quote
I recomputed the examples:
LIB"sing.lib";
ring r = 0,(x,y,z),ds;
poly f = x2 + y3 + z3 +zy;
poly g = x2 + y3 + y4 +yz2;
milnor(f); tjurina(f); //1
milnor(g); tjurina(g); //4

The answer is correct since f is contained in the ideal of the partials.
f is an A_1 and g a D_4 singularity. You get this by applying classify
from classify.lib.
Post Posted: Thu Jan 25, 2007 5:25 pm
greuel
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Please provide the full Singular input for your examples.
Post Posted: Sat Dec 09, 2006 1:53 am
kad
  Post subject:  milnor and tjurina numbers  Reply with quote
Bonjour,


can you me say why the procedure milnor and tjurina gives the same numbers for

{x^{2} + y^{3} + z^{3} +zy=0} or

{x^{2} + y^{3} + y^{4} +yz^{2}=0} ?

thanks.
kaddar.
Post Posted: Wed Oct 04, 2006 11:39 am


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