10 papers
On Picard groups and Jacobians of directed graphs
Jaiung Jun, Youngsu Kim, Matthew Pisano
The Picard group of an undirected graph is a finitely generated abelian group, and the Jacobian is the torsion subgroup of the Picard group. These groups can be computed by using t…
Computing multiplicity sequences
Justin Chen, Youngsu Kim, Jonathan Montaño
The MultiplicitySequence package for Macaulay2 computes the multiplicity sequence of a graded ideal in a standard graded ring over a field, as well as several invariants of monomia…
Log canonical thresholds of generic links of determinantal varieties
Youngsu Kim, Lance Edward Miller, Wenbo Niu
We show that the log canonical threshold of a generic determinantal variety and its generic link are the same.
A note on Non-Noetherian Cohen-Macaulay rings
Youngsu Kim, Andrew Walker
In this note, we study the Cohen-Macaulayness of non-Noetherian rings. We show that Hochster's celebrated theorem that a finitely generated normal semigroup ring is Cohen-Macaulay…
Equations defining certain graphs
Youngsu Kim, Vivek Mukundan
Consider the rational map defined by homogeneous polynomials $f_0,\dots,f…
A note on Itoh (e)-Valuation Rings of and Ideal
Youngsu Kim, Louis J. Ratliff, David E. Rush
Let be a regular proper ideal in a Noetherian ring , let be an integer, let (where…
Blowing Up Finitely Supported Complete Ideals in a Regular Local Ring
William Heinzer, Youngsu Kim, Matthew Toeniskoetter
Let I be a finitely supported complete m-primary ideal of a regular local ring (R, m). We consider singularities of the normalization of the blow-up Proj R[It] of I. A theorem of L…
Graded-irreducible modules are irreducible
Justin Chen, Youngsu Kim
We show that if a graded submodule of a Noetherian module cannot be written as a proper intersection of graded submodules, then it cannot be written as a proper intersection of sub…
Quasi-Gorensteinness of extended Rees algebras
Youngsu Kim
Let be a Noetherian local ring and an -ideal. It is well-known that if the associated graded ring $\gr_I(R)$ is Cohen-Macaulay (Gorenstein), then so is , but the conv…
On the Equality of Ordinary and Symbolic Powers of Ideals
Aline Hosry, Youngsu Kim, Javid Validashti
We consider the following question concerning the equality of ordinary and symbolic powers of ideals. In a regular local ring, if the ordinary and symbolic powers of a one-dimensio…