5 papers
A Linear Bound on the Projective Dimension of Height 3 Quadratic Ideals
Zachary Greif, Paolo Mantero, Jason McCullough
In 2016, Ananyan and Hochster gave the first proof of a positive answer to Stillman's Question, which asked for a bound on the projective dimension of a graded polynomial ideal pur…
Focal matroids of covers and homological properties of matroids
Paolo Mantero, Vinh Nguyen
In this paper we prove that the Stanley--Reisner ideal or cover ideal of a matroid is minimally resolvable by iterated mapping cones. As a technical tool for this purpose, we i…
Rational symbolic powers of ideals
Souvik Dey, Tai Huy Ha, Dipendranath Mahato +1
We introduce and study rational symbolic powers of ideals in Noetherian rings. We give membership criteria for rational symbolic powers and discuss settings where they agree with i…
Slightly mixed symbolic powers of matroids are locally glicci
Paolo Mantero, Vinh Nguyen
Let $\M$ be a matroid, and let $I_{\M}$ be either the Stanley--Reisner or the cover ideal of $\M$. In this paper we prove that for any matroid $\M$ on , any $\ell\in \ZZ_+$, a…
Ordinary and symbolic powers of matroids via polarization
Justin Lyle, Paolo Mantero
In this paper, we propose a uniform approach to tackle problems about squarefree monomial ideals whose powers have good properties. We employ this approach to achieve a twofold goa…