On the Gorenstein Property of Rees Algebras.
We prove a recent conjecture of S. Lvovski concerning the periodicity behaviour of top Betti numbers of general finite subsets with large cardinality of an irreducible curve C ⊂ ℙⁿ.
We study semigroups of labellings associated to a graph. These generalise the Jukes-Cantor model and phylogenetic toric varieties defined in [Buczynska W., Phylogenetic toric varieties on graphs, J. Algebraic Combin., 2012, 35(3), 421–460]. Our main theorem bounds the degree of the generators of the semigroup by g + 1 when the graph has first Betti number g. Also, we provide a series of examples where the bound is sharp.
Here we show the existence of strong restrictions for the Hilbert function of zerodimensional curvilinear subschemes of P n with one point as support and with high regularity index.
We study, in certain cases, the notions of finiteness and stability of the set of associated primes and vanishing of the homogeneous pieces of graded generalized local cohomology modules.