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EnglishLet I be the defining ideal of a smooth complete intersection space curve C with defining equations of degrees a and b. We use the partial elimination ideals introduced by Mark Green to show that the lexicographic generic initial ideal of I has Castelnuovo–Mumford regularity 1 + ab(a − 1)(b − 1)/2 with the exception of the case a=b=2, where the regularity is 4. Note that ab(a − 1)(b − 1)/2 is exactly the number of singular points of a general projection of C to the plane. Additionally, we show that for any term ordering τ, the generic initial ideal of a generic set of points in P^r is a τ -segment ideal.
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| Titolo: | Generic initial ideals of points and curves |
| Autori: | |
| Data di pubblicazione: | 2005 |
| Rivista: | |
| Abstract: | Let I be the defining ideal of a smooth complete intersection space curve C with defining equations of degrees a and b. We use the partial elimination ideals introduced by Mark Green to show that the lexicographic generic initial ideal of I has Castelnuovo–Mumford regularity 1 + ab(a − 1)(b − 1)/2 with the exception of the case a=b=2, where the regularity is 4. Note that ab(a − 1)(b − 1)/2 is exactly the number of singular points of a general projection of C to the plane. Additionally, we show that for any term ordering τ, the generic initial ideal of a generic set of points in P^r is a τ -segment ideal. |
| Handle: | http://hdl.handle.net/11567/208159 |
| Appare nelle tipologie: | 01.01 - Articolo su rivista |
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