Alastair Craw

collaborators

5 papers

math.AG2026

The Cautis-Logvinenko conjecture

Alastair Craw, Hsueh-Yung Lin, Ryo Yamagishi

For a finite subgroup $G \subset SL (3, C)$ , the Cautis--Logvinenko conjecture states that for each nontrivial irreducible representation $ρ$ of $G$ , the image…

math.AG2026

Hilbert schemes of points on canonical surfaces

Alastair Craw, Ryo Yamagishi

For $n \geq 1$ , we investigate the Hilbert scheme of $n$ -points on a surface $S$ with canonical singularities. We generalise the well-known theorem of Fogarty by showing that the un…

math.AG2025

The Le Bruyn-Procesi theorem following Lusztig

Alastair Craw, Ryo Yamagishi

For any quiver $Q$ and dimension vector $v$ , Le Bruyn-Procesi proved that the invariant ring for the action of the change of basis group on the space of representations $\text{Rep}…

math.AG2025

Birational geometry of quiver varieties and other GIT quotients

Gwyn Bellamy, Alastair Craw, Travis Schedler

We prove that all projective crepant resolutions of Nakajima quiver varieties satisfying natural conditions are also Nakajima quiver varieties. More generally, we classify the smal…

math.AG2025

Hilbert schemes for crepant partial resolutions

Alastair Craw, Ruth Wye

For $n \geq 1$ , we construct the underlying reduced subscheme of the Hilbert scheme of $n$ points on any crepant partial resolution of a Kleinian singularity as a Nakajima quiver va…