We determine the Castelnuovo-Mumford regularity of binomial edge ideals complement reducible graphs (cographs). For cographs with $n$ vertices maximum grows as $2n/3$. also bound by graph theoretic invariants and construct a family counterexamples to conjecture Hibi Matsuda.

We give an explicit formula for the degree of Grothendieck polynomial a Grassmannian permutation and closely related Castelnuovo-Mumford regularity Schubert determinantal ideal permutation. then provide counterexample to conjecture Kummini-Lakshmibai-Sastry-Seshadri on regularities standard open patches particular varieties show that our work gives rise alternate in these cases. end with new <i...

We provide a bound on the Θ-regularity of an arbitrary reduced and irreducible curve embedded in a polarized abelian variety in terms of its degree and codimension. This is an “abelian” version of Gruson–Lazarsfeld–Peskine’s bound on the Castelnuovo–Mumford regularity of a non-degenerate curve embedded in a projective space. As an application, we provide a Castelnuovo type bound for the genus o...

New upper bounds on the first and second Hilbert coefficients of a Cohen-Macaulay module over local ring are given. Characterizations provided for some to be attained. The characterizations given in terms series as well Castelnuovo-Mumford regularity associated graded module.

Let A A be a noetherian connected graded algebra. We introduce and study homological invariants that are weighted sums of the internal ...