Let I denote an ideal of a local Gorenstein ring (R, m). Then we show that the local cohomology module H I (R), c = height I, is indecomposable if and only if V (Id) is connected in codimension one. Here Id denotes the intersection of the highest dimensional primary components of I. This is a partial extension of a result shown by Hochster and Huneke in the case I the maximal ideal. Moreover th...

Abstract We study locally conformally balanced metrics on almost abelian Lie algebras, namely solvable algebras admitting an ideal of codimension one, providing characterizations in every dimension. Moreover, we classify six-dimensional and some compatibility results between different types special Hermitian groups their compact quotients. end by classifying hyperkähler structures.

An unpublished example due to Joe Harris from 1983 (or earlier) gave two smooth space curves with the same Hilbert function, but one of the curves was arithmetically CohenMacaulay (ACM) and the other was not. Starting with an arbitrary homogeneous ideal in any number of variables, we give two constructions, each of which produces, using a finite number of basic double links, an ideal with the H...

We prove that every finitely generated Lie algebra containing a nilpotent ideal of class c and finite codimension n has Gelfand-Kirillov dimension at most cn. In particular, finitely generated virtually nilpotent Lie algebras have polynomial growth.