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| milnor and tjurina numbers https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1552 |
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| Author: | kad [ Wed Oct 04, 2006 11:39 am ] |
| Post subject: | milnor and tjurina numbers |
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. |
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| Author: | greuel [ Sat Dec 09, 2006 1:53 am ] |
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Please provide the full Singular input for your examples. |
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| Author: | greuel [ Thu Jan 25, 2007 5:25 pm ] |
| Post subject: | |
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. |
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| Author: | renzo [ Sat Feb 03, 2007 1:30 am ] |
| Post subject: | |
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. |
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