Timeline for What is the type of the surfaces $x^5 - y^5 + z^2 + x=0$ and $x^5 - y^5 + z^2 + x+1=0$?
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14 events
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| Sep 24, 2017 at 1:00 | comment | added | D.W. | Cross-posted: math.stackexchange.com/q/1401214/14578. Please do not post the same question on multiple sites. Each community should have an honest shot at answering without anybody's time being wasted. | |
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Aug 20, 2015 at 6:53 | vote | accept | joro | ||
| Aug 19, 2015 at 14:39 | comment | added | joro | @kantelope Many thanks, this looks interesting :-) | |
| Aug 19, 2015 at 11:19 | comment | added | kantelope | For Magma, somehow example H119E12 should give the idea of how to resolve singularities, but it is beyond my ability currently. magma.maths.usyd.edu.au/magma/handbook/text/1355#14997 | |
| Aug 19, 2015 at 9:53 | comment | added | joro | @AlexDegtyarev I meant that the singularity is of multiplicity $2$ according to magma if I have done it right. Thank you for the answer. | |
| Aug 19, 2015 at 9:43 | comment | added | Alex Degtyarev | I don't understand what you mean. I made it an answer. | |
| Aug 19, 2015 at 9:43 | answer | added | Alex Degtyarev | timeline score: 4 | |
| Aug 19, 2015 at 9:12 | comment | added | joro | @AlexDegtyarev According to Magma it is of multiplicity $2$ if I have done it right. | |
| Aug 19, 2015 at 9:05 | comment | added | Alex Degtyarev | The first one would be $z_0z_1^5-z_0z_2^5+z_0^5z_1=0$ in homogeneous coordinates. | |
| Aug 19, 2015 at 9:04 | comment | added | Alex Degtyarev | Just drop $z$ from the equations, and add the line at infinity to the resulting affine quintic. Say, the first one is obviously nonsingular in the affine part, but you should also check the singularities at infinity. | |
| Aug 19, 2015 at 9:01 | comment | added | joro | @AlexDegtyarev Thank you, my wild guess was this. If you don't plan to do it would you please give the sextics to check them? | |
| Aug 19, 2015 at 8:59 | comment | added | Alex Degtyarev | I would say that both are $K3$: they are double planes ramified at sextics (the order $5$ curves in $x$, $y$ and the line at infinity). One should only check carefully that these sextics have simple singulrities. | |
| Aug 19, 2015 at 8:19 | history | asked | joro | CC BY-SA 3.0 |