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TitleGeneric initial ideals of points and curves
Author(s) Aldo Conca, Jessica Sidman
TypeArticle in Journal
AbstractLet 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 + a b ( a − 1 ) ( b − 1 ) / 2 with the exception of the case a = b = 2 , where the regularity is 4. Note that a b ( 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.
KeywordsGeneric initial ideal, Curves, Points, Lexicographic term order
URL http://www.sciencedirect.com/science/article/pii/S0747717105000714
JournalJournal of Symbolic Computation
Pages1023 - 1038
Translation No
Refereed No