Timeline for Surfaces singular along a curve
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 7, 2014 at 19:27 | comment | added | abx | You just need the degree (by Riemann-Roch), that is $c_1$, and that's standard: if $E$ has degree $d$ and rank 2, $\mathrm{Sym}^pE$ has degree $\frac{1}{2}dp(p+1) $ (by the splitting principle you just need to check that when $E=L\oplus M$, then it is straightforward). | |
| Apr 7, 2014 at 16:35 | comment | added | Lalit Jain | Can you say a quick word about how you compute the Euler characteristics of the symmetric powers that pop up? | |
| Apr 7, 2014 at 5:11 | comment | added | abx | I have edited the question and treated the general case. | |
| Apr 7, 2014 at 5:11 | history | edited | abx | CC BY-SA 3.0 |
Treated the general case instead of a particular case
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| Apr 6, 2014 at 19:17 | comment | added | abx | No, sorry, I just did it for $\beta=2$. The same method works for any $\beta$ but the computation becomes tedious. The rest of the argument adapts immediately. | |
| Apr 6, 2014 at 17:24 | comment | added | user47036 | Thank you for the answer. I just do not understand where you take into account the multiplicity $\beta$ along $C$. It seems to me that in this way you compute the dimension of the system of surfaces having multiplicity $2$ along $C$. Am I missing something? | |
| Apr 6, 2014 at 13:28 | history | edited | abx | CC BY-SA 3.0 |
edited body
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| Apr 6, 2014 at 13:09 | history | answered | abx | CC BY-SA 3.0 |