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...

Projective monomial curves correspond to rings generated by monomials of the same degree in two variables. Such always have finite Macaulayfication. We show how characterize Buchsbaumness and Castelnuovo-Mumford regularity these means their Macaulayfication, we use this method study estimate large classes non-smooth terms given monomials.

Abstract We provide a homological construction of unitary simple modules Cherednik and Hecke algebras type A via BGG resolutions, solving conjecture Berkesch–Griffeth–Sam. vastly generalize the its solution to cyclotomic over arbitrary ground fields, calculate Betti numbers Castelnuovo–Mumford regularity certain symmetric linear subspace arrangements.

There are two motivating questions in [M. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N. Terai and S. Yassemi, arXiv:1006.1087v1] J. Pure Appl. Algebra, 215(10) (2011), 2473-2480] about Castelnuovo-Mumford regularity vertex decomposability of simple graphs. In this paper, we give negative answers to the by providing counterexamples.

Abstract Let I be a homogeneous ideal in polynomial ring S . In this paper, we extend the study of asymptotic behavior minimum distance function δ and give bounds for its stabilization point, r , when is an F -pure or square-free monomial ideal. These are related with dimension Castelnuovo–Mumford regularity