B. Baily

activity

20222026

collaborators

7 papers

math.AG2026

Closedness of bounded strength and partition rank loci

Benjamin Baily, Alessandro Danelon

We show the existence of a quartic form of strength $3$ in the closure of the strength at most $2$ locus, answering a question of Ballico--Bik--Oneto--Ventura in the negative. In t…

math.AC2026

Homogeneous ideals with minimal singularity thresholds

Benjamin Baily

Let $(O_{n}, m)$ denote the ring of germs of holomorphic functions $C^{n} \to C$ , and let $I \subseteq O_{n}$ be an $m$ -primary…

math.AC2026

Extremal F-thresholds in regular local rings

Benjamin Baily

Let $(R, m)$ be a regular local ring of characteristic $p > 0$ . Among all proper ideals $a \subseteq R$ with a fixed order of vanishing $\text{ord}_{\mathfrak{…

math.AC2025

On lower bounds for the F-pure threshold of equigenerated ideals

Benjamin Baily

Let $k$ be a field of positive characteristic and $R = k [x_{0}, \dots, x_{n}]$ . We consider ideals $I \subseteq R$ generated by homogeneous polynomials of degree $d$ . Takagi and Watanabe…

math.AC2025

On deformation of perfectoid purity in Gorenstein domains

Benjamin Baily, Karina Dovgodko, Austyn Simpson +1

If $(R, m)$ is a complete local ring of mixed characteristic $(0, p)$ and $R / pR$ is an $F$ -pure Gorenstein domain, we find a sufficient condition for $R$ to be perfectoid…

math.NT2024

Strength is bounded linearly by Birch rank

Benjamin Baily, Amichai Lampert

Let $f$ be a homogeneous polynomial over a field. For many fields, including number fields and function fields, we prove that the strength of $f$ is bounded above by a constant mul…

math.AC2022

Completions of Countable Excellent Local Rings in Equal Characteristic Zero

B. Baily, S. Loepp

We characterize which complete local (Noetherian) rings T containing the rationals are the completion of a countable excellent local ring S. We also discuss the possibilities for t…