16 citations · 42 across the 10 of their papers we have counts for
11 papers
On basic double G-links of squarefree monomial ideals
Patricia Klein, Matthew Koban, Jenna Rajchgot
Nagel and Römer introduced the class of weakly vertex decomposable simplicial complexes, which include matroid, shifted, and Gorenstein complexes as well as vertex decomposable com…
Differential operators, retracts, and toric face rings
Christine Berkesch, C-Y. Jean Chan, Patricia Klein +3
We give explicit descriptions of rings of differential operators of toric face rings in characteristic . For quotients of normal affine semigroup rings by radical monomial ideal…
Bumpless pipe dreams encode Gröbner geometry of Schubert polynomials
Patricia Klein, Anna Weigandt
In their study of infinite flag varieties, Lam, Lee, and Shimozono (2021) introduced bumpless pipe dreams in a new combinatorial formula for double Schubert polynomials. These poly…
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…
Homological and combinatorial aspects of virtually Cohen--Macaulay sheaves
Christine Berkesch, Patricia Klein, Michael C. Loper +1
When studying a graded module over the Cox ring of a smooth projective toric variety , there are two standard types of resolutions commonly used to glean information: free r…
Diagonal degenerations of matrix Schubert varieties
Patricia Klein
Knutson and Miller (2005) established a connection between the anti-diagonal Gröbner degenerations of matrix Schubert varieties and the pre-existing combinatorics of pipe dreams. T…
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…
Geometric vertex decomposition and liaison
Patricia Klein, Jenna Rajchgot
Geometric vertex decomposition and liaison are two frameworks that have been used to produce similar results about similar families of algebraic varieties. In this paper, we establ…
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…
Characterizing finite length local cohomology in terms of bounds on Koszul cohomology
Patricia Klein
Let be a local ring. We give a characterization of -modules whose local cohomology is finite length up to some index in terms of asymptotic vanishing of Koszul co…
Lech's inequality, the Stückrad--Vogel conjecture, and uniform behavior of Koszul homology
Patricia Klein, Linquan Ma, Pham Hung Quy +2
Let be a Noetherian local ring, and let be a finitely generated -module of dimension . We prove that the set $\left\{\frac{l(M/IM)}{e(I, M)} \right\}_{…