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Hello,

Does anybody know a reference for the following result: $d\ge 5$ points of $\mathbb P^2$ fail to impose independent conditions on curves of degree $d-3$ if and only if at least $d-1$ of these points are collinear. As usual, "fail to impose independent conditions" means $h^0(\mathcal I_D(d-3))>h^0(\mathcal O_{\mathbb P^2}(d-3))-d$ , where $D$ is the set of points in question.

I have written up a proof of that, but of course one should give a reference if there is one, which is in my opinion quite probable.

Thank you in advance,
Serge

edited Jan 1 at 18:25

asked Jan 1 at 16:12

Serge Lvovski
1,032●1●9

ab · Accepted Answer · 2013-01-01 18:04:16Z UTC

3

You mean "curves of degree $d-3$". A reference (for a more general result) is: D. Eisenbud, M. Green, and J. Harris, CayleyBacharach theorems and conjectures, Bull. Amer. Math. Soc. 33 (1996), 295–324.

answered Jan 1 at 18:04

ab
46●1

$d-3$, yes. Many thanks both for the correction and the reference! – Serge Lvovski Jan 1 at 18:43

Points in the plane imposing independent conditions: reference request

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