Timeline for Singularities of the union of two smooth curves
Current License: CC BY-SA 3.0
9 events
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| May 3, 2018 at 21:30 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 3, 2018 at 19:11 | answer | added | Xavier49 | timeline score: 2 | |
| Apr 2, 2018 at 7:00 | comment | added | Xavier49 | @Mohan Thanks! Yes, but the "easily" part is not so easy for me, because I do not know how to tell when too singularities are 'the same', I mean I suppose there are some equivalence relations but I do not know which they are. By example one has the singularity $(x-y^a)(x+y^b)=0$, with say $a \leq b$. By expanding that polynomial, my intuition tells me that this is a $A_{2a}$ singularity, but I would like to understand rigorously why. More generally with e.g. $(x+vy^a)(x+uy^b)=0$, where $u,v$ are non equal constants. | |
| Apr 1, 2018 at 18:35 | comment | added | Mohan | At any point $P\in C_1\cup C_2$, in the completion of the local ring of the surface, you can easily see that $C_1\cup C_2$ is given by $x(x-y^n)=0$ for suitable choices of parameters $x,y$. So, if characteristic is not 2, this can be changed to $x^2-y^{2n}=0$ which is what you are claiming. | |
| Apr 1, 2018 at 17:04 | comment | added | Xavier49 | @Mohan : $A_n$ singularity has equation $y^2-x^{n+1}=0$ | |
| Apr 1, 2018 at 17:04 | history | edited | Xavier49 | CC BY-SA 3.0 |
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| Apr 1, 2018 at 16:06 | history | edited | Xavier49 | CC BY-SA 3.0 |
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| Apr 1, 2018 at 15:43 | comment | added | Mohan | What is $A_n$ singularity for you? | |
| Apr 1, 2018 at 10:37 | history | asked | Xavier49 | CC BY-SA 3.0 |