Heavy quark asymmetries with DELPHI

The measurements of the forward-backward asymmetry in Z -> c cbar and Z -> b bbar decays are among the most precise determinations of sin^2(theta)_W. In this paper the results obtained by the DELPHI experiment at LEP with three different analyses are reviewed together with the impact of the combined LEP result on the global Electroweak fit.Comment: 7 pages, RevTeX, fonts changed in 2 eps file

The Lefschetz properties of monomial complete intersections in positive characteristic

Stanley proved that, in characteristic zero, all artinian monomial complete intersections have the strong Lefschetz property. We provide a positive characteristic complement to Stanley's result in the case of artinian monomial complete intersections generated by monomials all of the same degree, and also for arbitrary artinian monomial complete intersections in characteristic two. To establish these results, we first prove an a priori lower bound on the characteristics that guarantee the Lefschetz properties. We then use a variety of techniques to complete the classifications.Comment: 18 page

Unimodal Gorenstein h-vectors without the Stanley-Iarrobino property

The study of the $h$-vectors of graded Gorenstein algebras is an important topic in combinatorial commutative algebra, which despite the large amount of literature produced during the last several years, still presents many interesting open questions. In this note, we commence a study of those unimodal Gorenstein $h$-vectors that do \emph{not} satisfy the Stanley-Iarrobino property. Our main results, which are characteristic free, show that such $h$-vectors exist: 1) In socle degree $e$ if and only if $e\ge 6$; and 2) In every codimension five or greater. The main case that remains open is that of codimension four, where no Gorenstein $h$-vector is known without the Stanley-Iarrobino property. We conclude by proposing the following very general conjecture: The existence of any arbitrary level $h$-vector is \emph{independent} of the characteristic of the base field.Comment: A few minor revisions. Final version to appear in Comm. Algebr