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arXiv · 1708.03969

On coherent sheaves of small length on the affine plane

Riccardo Moschetti·Andrea T. Ricolfi
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Abstract

We classify coherent modules on $k[x,y]$ of length at most $4$ and supported at the origin. We compare our calculation with the motivic class of the moduli stack parametrizing such modules, extracted from the Feit-Fine formula. We observe that the natural torus action on this stack has finitely many fixed points, corresponding to connected skew Ferrers diagrams.

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Riccardo Moschetti, Andrea T. Ricolfi. 2017-08-13. On coherent sheaves of small length on the affine plane. https://arxiv.org/abs/1708.03969

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