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



Points in the plane imposing independent conditions: reference request
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.


