Mathematics – Commutative Algebra
Scientific paper
2008-07-24
Mathematics
Commutative Algebra
14 pages, improved version, some more examples
Scientific paper
The stratum St(J,<) (the homogeneous stratum Sth(J,<) respectively) of a monomial ideal J in a polynomial ring R is the family of all (homogeneous) ideals of R whose initial ideal with respect to the term order < is J. St(J,<) and Sth(J,<) have a natural structure of affine schemes. Moreover they are homogeneous w.r.t. a non-standard grading called level. This property allows us to draw consequences that are interesting from both a theoretical and a computational point of view. For instance a smooth stratum is always isomorphic to an affine space (Corollary 3.6). As applications, in Sec. 5 we prove that strata and homogeneous strata w.r.t. any term ordering < of every saturated Lex-segment ideal J are smooth. For Sth(J,Lex) we also give a formula for the dimension. In the same way in Sec. 6 we consider any ideal R in k[x0,..., xn] generated by a saturated RevLex-segment ideal in k[x,y,z]. We also prove that Sth(R,RevLex) is smooth and give a formula for its dimension.
Roggero Margherita
Terracini Lea
No associations
LandOfFree
Ideals with an assigned initial ideal does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Ideals with an assigned initial ideal, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ideals with an assigned initial ideal will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-676658