Aron Simis

TL;DR: In this paper, the authors studied the Cohen-Macaulay behavior of the Koszul homology of the quotient ring R/I(G) of a polynomial ring R. The main results are assertions about the Cohen -Macauley behaviour of I(G), and how normality or Cohen-macaulayness of one of the algebras can be read off the properties of the graph or in the other algebra.

TL;DR: In this article, the authors studied the relationship between the arithmetical properties of the Rees ring, 9(I), and the symmetric algebra Sym(l), of an ideal I (and some of their fibers) and the depth properties of H,(I; R), on a set of generators of I.

TL;DR: In this paper, the integral closure of the monomial subring of a polynomial ring over a field k is described, where the squarefree monomials of degree two defining the edges of the graph are defined.

TL;DR: In this paper, the existence of irreducible homaloidal hypersurfaces in projective space was studied and an infinite family of determinantal hypersurface based on a certain degeneration of a generic Hankel matrix was introduced.