Zero-dimensional subschemes of projective spaces related to double points of linear subspaces and to fattening directions
Abstract
Fix a linear subspace 
and a linearly independent set 
. Let 
or 
with 
and 
, be the zero-dimensional subscheme of 
union of all double points 
, 
, of (not of 
if 
). We study the Hilbert function of 
and of general unions in of these schemes. In characteristic 
we determine the Hilbert function of general unions of 
(easy), of 
and, if 
, general unions of schemes 
and
and a linearly independent set . Let or with and , be the zero-dimensional subscheme of union of all double points , , of (not of if ). We study the Hilbert function of and of general unions in of these schemes. In characteristic we determine the Hilbert function of general unions of (easy), of and, if , general unions of schemes and Keywords:
zero-dimensional scheme; Hilbert function; postulation
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