We show that the GVC (generalized vanishing conjecture) holds for the differential operator and all polynomials , where is any polynomial over the base field. The GVC arose from the study of the Jacobian conjecture.
In this paper, we give a geometrization and a generalization of a lemma of differential Galois theory, used by Singer and van der Put in their reference book. This geometrization, in addition of giving a nice insight on this result, offers us the opportunity to investigate several points of differential algebra and differential algebraic geometry. We study the class of simple Δ-schemes and prove that they all have a coarse space of leaves. Furthermore, instead of considering schemes endowed with...
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.