We consider the problem of determining the Hilbert function of projective schemes X which are the generic union of s lines and one m-multiple point. We completely solve this problem for any s and m when n >3. When n=3 we find several defective such schemes and conjecture that they are the only ones. We verify this conjecture in several cases.
On the Hilbert function of lines union one non-reduced point
CATALISANO, MARIA VIRGINIA;GERAMITA, ANTHONY VITO
2016
Abstract
We consider the problem of determining the Hilbert function of projective schemes X which are the generic union of s lines and one m-multiple point. We completely solve this problem for any s and m when n >3. When n=3 we find several defective such schemes and conjecture that they are the only ones. We verify this conjecture in several cases.
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