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Let
be a collection of
distinct points. Then the number
of conditions imposed by
on forms of degree
is called the Hilbert function
of
.
If curves
and
of degrees
and
meet in a collection
of
points, then for any
,
the number
of conditions imposed by
on forms of degree
is independent of
and
and
is given by
References
Eisenbud, D.; Green, M.; and Harris, J. ``Cayley-Bacharach Theorems and Conjectures.'' Bull. Amer. Math. Soc.
33, 295-324, 1996.