Patricia Klein

activity

20182021

collaborators

6 papers

math.AC2021

An illustrated view of differential operators of a reduced quotient of an affine semigroup ring

Christine Berkesch, C-Y. Jean Chan, Patricia Klein +3

Through examples, we illustrate how to compute differential operators on a quotient of an affine semigroup ring by a radical monomial ideal, when working over an algebraically clos…

math.AC2020

Homological and combinatorial aspects of virtually Cohen--Macaulay sheaves

Christine Berkesch, Patricia Klein, Michael C. Loper +1

When studying a graded module $M$ over the Cox ring of a smooth projective toric variety $X$ , there are two standard types of resolutions commonly used to glean information: free r…

math.AC2020

Toric double determinantal varieties

Alexander Blose, Patricia Klein, Owen McGrath +1

We examine Li's double determinantal varieties in the special case that they are toric. We recover from the general double determinantal varieties case, via a more elementary argum…

math.AC2019

Gröbner bases and the Cohen-Macaulay property of Li's double determinantal varieties

Nathan Fieldsteel, Patricia Klein

We consider double determinantal varieties, a special case of Nakajima quiver varieties. Li conjectured that double determinantal varieties are normal, irreducible, Cohen-Macaulay…

math.AC2018

Characterizing finite length local cohomology in terms of bounds on Koszul cohomology

Patricia Klein

Let $(R, m, κ)$ be a local ring. We give a characterization of $R$ -modules $M$ whose local cohomology is finite length up to some index in terms of asymptotic vanishing of Koszul co…

math.AC2018

Lech's inequality, the Stückrad--Vogel conjecture, and uniform behavior of Koszul homology

Patricia Klein, Linquan Ma, Pham Hung Quy +2

Let $(R, m)$ be a Noetherian local ring, and let $M$ be a finitely generated $R$ -module of dimension $d$ . We prove that the set $\left\{\frac{l(M/IM)}{e(I, M)} \right\}_{…