Mathematics – Commutative Algebra
Scientific paper
2006-08-22
Mathematics
Commutative Algebra
29 pages, 3 figures, Positive characteristic results incorporated into main body of paper
Scientific paper
Symbolic powers are studied in the combinatorial context of monomial ideals. When the ideals are generated by quadratic squarefree monomials, the generators of the symbolic powers are obstructions to vertex covering in the associated graph and its blowups. As a result, perfect graphs play an important role in the theory, dual to the role played by perfect graphs in the theory of secants of monomial ideals. We use Gr\"obner degenerations as a tool to reduce questions about symbolic powers of arbitrary ideals to the monomial case. Among the applications are a new, unified approach to the Gr\"obner bases of symbolic powers of determinantal and Pfaffian ideals.
No associations
LandOfFree
Combinatorial symbolic powers 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 Combinatorial symbolic powers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Combinatorial symbolic powers will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-572373