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math.AC2026
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…
math.AC2026
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…