Nowhere-torsion canonical bundles on blowups of the projective plane

Determine whether the canonical bundle is nowhere torsion for the blowup of $\mathbb{P}^2$ at more than nine very general points.

Background

The paper gives several classes of blowups of P2\mathbb{P}^2 whose canonical bundles are nowhere torsion. In particular, it records the known result for nine very general points over C\mathbb{C}, where neither the canonical bundle nor its inverse is big.

The text identifies the extension to more than nine very general points as an unresolved question. Establishing it would provide further examples to which the paper’s derived reconstruction theorem applies, even though the canonical bundle is not covered by the stronger tensor-generation criteria.

References

The authors contemplate in Remark 3.3 whether it could be true that $\omega_X$ is nowhere torsion when $X$ is a blow up of $\mathbb{P}2$ in $n >9$ very general points as well.

— Bondal--Orlov reconstruction for tame stacks with trivial generic stabilizer  (2609.28867 - Ito et al., 24 Sep 2026) in Example, item (3), in Section 2.3.1 (Blow-ups)