Timeline for Global sections of the structure sheaf of a non-reduced projective scheme
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Dec 2, 2013 at 9:59 | comment | added | Naga Venkata | No. The ideal of $2l+C'$ does not contain the ideal of the plane. See "Le Schema de Hilbert des Courbes gauches localement Cohen-Macualay n'est (presque) jamais reduit" by M Martin-Descamps and D. Perrin Proposition $0.6$ for such examples. | |
| Dec 2, 2013 at 8:51 | comment | added | abx | Sorry I don't get it. You say that "$C'$ is a reduced plane curve lying on the same plane as $l$". Doesn't that mean that $C$ is the curve $2l+C'$ in that plane? | |
| Dec 2, 2013 at 8:37 | comment | added | Naga Venkata | $C$ is not necessarily a plane curve. I do not know how else to write it. I meant that the curve is the scheme associated to an effective divisor on a surface. Using the adjunction formula one sees that the arithmetic genus depends on the degree of the surface. For example take a smooth surface containing $l, C'$. This will also contain the curve $2l+C'$ as a Weil divisor. But the genus depends on the degree of the surface. | |
| Dec 2, 2013 at 6:21 | history | answered | abx | CC BY-SA 3.0 |