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TitleCombinatorial symbolic powers
Author(s) Seth Sullivant
TypeArticle in Journal
AbstractSymbolic 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 Gröbner 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 Gröbner bases of symbolic powers of determinantal and Pfaffian ideals.
KeywordsSymbolic power, Gröbner basis, Perfect graph, Edge ideal, Determinantal ideal
URL http://www.sciencedirect.com/science/article/pii/S0021869307005273
JournalJournal of Algebra
Pages115 - 142
Translation No
Refereed No