R. Hartshorne and A. Hirschowitz proved that a generic collection of lines on P^n, n>2, has bipolynomial Hilbert function. We extend this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., a union of schemes obtained by degenerating pairs of skew lines).
3-dimensional sundials
CATALISANO, MARIA VIRGINIA;GERAMITA, ANTHONY VITO
2011-01-01
Abstract
R. Hartshorne and A. Hirschowitz proved that a generic collection of lines on P^n, n>2, has bipolynomial Hilbert function. We extend this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., a union of schemes obtained by degenerating pairs of skew lines).
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