Higher Infinitesimal Neighbourhoods
We study the Hilbert function of thekth order neighbourhood of a collection Γ of points in linearly general position in Pn, writtenhPn(Γk,m). Our main results are the following bounds onhPn(Γk,k+1): If degΓ≥2n−k+1 thenhPn(Γk,k+1)≥hPn(Ck,k+1), whereC⊂Pnis a rational normal curve of degreen. If Γ is s...
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| Veröffentlicht in: | Journal of algebra 1998-07, Vol.205 (2), p.460-479 |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We study the Hilbert function of thekth order neighbourhood of a collection Γ of points in linearly general position in Pn, writtenhPn(Γk,m). Our main results are the following bounds onhPn(Γk,k+1):
If degΓ≥2n−k+1 thenhPn(Γk,k+1)≥hPn(Ck,k+1), whereC⊂Pnis a rational normal curve of degreen.
If Γ is sufficiently general ands=degΓ then and equality holds whenk=3. |
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| ISSN: | 0021-8693 1090-266X |
| DOI: | 10.1006/jabr.1997.7393 |