Thomas Polstra

collaborators

4 papers

math.AC2026

$F$ -injectivity does not imply $F$ -fullness in normal domains

Alessandro De Stefani, Thomas Polstra, Austyn Simpson

We construct examples of noetherian three-dimensional local geometrically normal domains of prime characteristic which are $F$ -injective but not $F$ -full. Along the way, we find ex…

math.AC2025

Strong $F$ -regularity and the Uniform Symbolic Topology Property

Thomas Polstra

We investigate the containment problem of symbolic and ordinary powers of ideals in a commutative Noetherian domain $R$ . Let $R$ be a normal domain of prime characteristic $p > 0$ th…

math.AC2025

Zariski-Nagata Theorems for Singularities and the Uniform Izumi-Rees Property

Thomas Polstra

We introduce and explore the Uniform Izumi-Rees Property in Noetherian rings with applications to multiplicity theory and containment relationships among symbolic powers of ideals.…

math.AG2025

Bertini's theorem for $F$ -rational $F$ -pure singularities

Alessandro De Stefani, Thomas Polstra, Austyn Simpson

Let $k$ be an algebraically closed field of characteristic $p > 0$ , and let $X \subseteq P_{k}^{n}$ be a quasi-projective variety that is $F$ -rational and $F$ -pure. We prove that…

F-injectivity does not imply F-fullness in normal domains

Strong F-regularity and the Uniform Symbolic Topology Property

Zariski-Nagata Theorems for Singularities and the Uniform Izumi-Rees Property

Bertini's theorem for F-rational F-pure singularities

$F$ -injectivity does not imply $F$ -fullness in normal domains

Strong $F$ -regularity and the Uniform Symbolic Topology Property

Bertini's theorem for $F$ -rational $F$ -pure singularities