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arXiv · 2604.15098

Tangent bundle of punctual Hilbert scheme and distinguishing products of varieties

Supravat Sarkar
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Abstract

We describe the indecomposable components of the tangent bundle of the punctual Hilbert scheme of a smooth projective surface. As an application, we prove a recent conjecture about classification of products of punctual Hilbert schemes of smooth projective surfaces. We also determine when two products of symmetric powers of a smooth variety can be isomorphic. As a key step in our proof, we give a new characterization of abelian varieties, which states that in dimension $\geq 2$, a smooth complex projective variety whose tangent bundle is trivial upto a line bundle twist is an abelian variety.

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Supravat Sarkar. 2026-04-16. Tangent bundle of punctual Hilbert scheme and distinguishing products of varieties. https://arxiv.org/abs/2604.15098

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