61,736 research outputs found
Combinatorial symbolic powers
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.Comment: 29 pages, 3 figures, Positive characteristic results incorporated
into main body of pape
Products of Borel fixed ideals of maximal minors
We study a large family of products of Borel fixed ideals of maximal minors.
We compute their initial ideals and primary decompositions, and show that they
have linear free resolutions. The main tools are an extension of straightening
law and a very surprising primary decomposition formula. We study also the
homological properties of associated multi-Rees algebra which are shown to be
Cohen-Macaulay, Koszul and defined by a Gr\"obner basis of quadrics
Multiplicities of Classical Varieties
The -multiplicity plays an important role in the intersection theory of
St\"uckrad-Vogel cycles, while recent developments confirm the connections
between the -multiplicity and equisingularity theory. In this paper
we establish, under some constraints, a relationship between the
-multiplicity of an ideal and the degree of its fiber cone. As a
consequence, we are able to compute the -multiplicity of all the ideals
defining rational normal scrolls. By using the standard monomial theory, we can
also compute the - and -multiplicity of ideals defining
determinantal varieties: The found quantities are integrals which, quite
surprisingly, are central in random matrix theory.Comment: 27 pages; to appear in Proc. London Math. So
Mapping and analysis of the current self- and co- regulatory framework of commercial communication aimed at minors
As the advertising sector has been very active in self-regulating commercial communication aimed at children, a patchwork of different rules and instruments exist, drafted by different self-regulatory organisations at international, European and national level. In order to determine the scope and contents of these rules, and hence, the actual level of protection of children, a structured mapping of these rules is needed. As such, this report aims to provide an overview of different categories of Alternative Regulatory Instruments(ARIs,such as self- and co-regulation regarding (new) advertising formats aimed at children. This report complements the first legal AdLit research report, which provided an overview of the legislative provisions in this domain.status: publishe
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