Combinatorial symbolic powers

JOURNAL OF ALGEBRA

卷:319

Article

Sullivant, Seth

关键词: symbolic power;    Grobner basis;    perfect graph;    edge ideal;    determinantal ideal;   

DOI  :  10.1016/j.jalgebra.2007.09.024

来源: Elsevier

【 摘 要 】

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 Grobner 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 Grobner bases of symbolic powers of determinantal and Pfaffian ideals. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free