Timeline for Analogues of the Weierstrass p function for higher genus compact Riemann surfaces
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Oct 28, 2009 at 10:08 | comment | added | David Lehavi | @administrator: The moduli of degree d curves is the number of monomials of degree d in 3 variables minus the dimension of GL_3, all in all: (d+2)(d+1)/2 - 9 (don't expect this to work for d < 3: too many automorphisms). Which is much smaller then 3g-3. | |
| Oct 28, 2009 at 1:05 | comment | added | solbap | @David Speyer: this is great, I was looking for an answer along these lines. Do you know of a good reference that goes into this in more detail? Also do you know if you restrict genus g = 1/2(d-1)(d-2) for d a positive integer if its possible to find an embedding and not just an immersion into P^2? | |
| Oct 28, 2009 at 1:00 | vote | accept | solbap | ||
| Oct 27, 2009 at 23:24 | comment | added | David Lehavi | The reason for P being so special in genus 1 - in my opinion at least - is that {1,P,P'} generate the ring of meromorphic functions on the curve (see e.g. Alain Robert's book). This goes against Riemann-Roch in higher genera. | |
| Oct 27, 2009 at 23:18 | history | edited | David E Speyer | CC BY-SA 2.5 |
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| Oct 27, 2009 at 22:48 | history | answered | David E Speyer | CC BY-SA 2.5 |