Blowups in tame monomial ideals
E. Faber, D.B. Westra
TL;DR
This paper investigates conditions under which blowups of affine space along monomial ideals are smooth, providing combinatorial criteria and exploring related smoothing procedures, monomial building sets, and permutohedra.
Contribution
It introduces a combinatorial criterion to determine smoothness of blowups along monomial ideals and applies it to various smoothing techniques and geometric structures.
Findings
Provided a criterion for smooth blowups in monomial ideals
Connected smoothing procedures to combinatorial structures like permutohedra
Analyzed the properties of tame monomial ideals in blowup contexts
Abstract
We study blowups of affine n-space with center an arbitrary monomial ideal and call monomial ideals that render smooth blowups tame ideals. We give a combinatorial criterion to decide whether the blowup is smooth and apply this criterion to discuss a smoothing procedure proposed by Rosenberg, monomial building sets and permutohedra.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Topological and Geometric Data Analysis · Algebraic Geometry and Number Theory