2 00 7 Generalized Test Ideals and Symbolic Powers
نویسنده
چکیده
Hochster and Huneke proved in [HH6] fine behaviors of symbolic powers of ideals in regular rings, using the theory of tight closure. In this paper, we use generalized test ideals, which are a characteristic p analogue of multiplier ideals, to give a slight generalization of Hochster-Huneke's results.
منابع مشابه
Generalized Test Ideals and Symbolic Powers
In [HH7], developing arguments in [HH5], Hochster and Huneke used classical tight closure techniques to prove a fine behavior of symbolic powers of ideals in regular rings. In this paper, we use generalized test ideals, which are a characteristic p analogue of multiplier ideals, to give a generalization of Hochster-Huneke's results.
متن کاملm at h . A C ] 2 2 A ug 2 00 6 COMBINATORIAL SYMBOLIC POWERS SETH
Symbolic powers of ideals 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 blow-ups. As a result, perfect graphs play an important role in the theory, dual to the role played by perfect graphs in the theory of seca...
متن کامل1 N ov 2 00 6 COMBINATORIAL SYMBOLIC POWERS
Symbolic powers of ideals 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 blow-ups. As a result, perfect graphs play an important role in the theory, dual to the role played by perfect graphs in the theory of seca...
متن کاملLinear Resolutions of Powers of Generalized Mixed Product Ideals
Let L be the generalized mixed product ideal induced by a monomial ideal I. In this paper we compute powers of the genearlized mixed product ideals and show that Lk have a linear resolution if and only if Ik have a linear resolution for all k. We also introduce the generalized mixed polymatroidal ideals and prove that powers and monomial localizations of a generalized mixed polymatroidal ideal...
متن کاملStudy and characterization of some classes of polymatroidal ideals
In this paper, the class of polymatroidal ideals are studied. In particular, we show that any polymatroidal ideal has a regular decomposition function, so we can give its explicit resolution. We also characterize generic polymatroidal ideals. Finally, we characterize monomial ideals which all their powers are generalized Cohen-Macaulay polymatroidal ideals.
متن کامل