On coherent sheaves of small length on the affine plane

JOURNAL OF ALGEBRA

卷:516

Article

关键词: Coherent sheaves;    Finite length modules;    Grothendieck ring of varieties;    Hilbert scheme of points;    Torus actions;   

DOI  :  10.1016/j.jalgebra.2018.09.028

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free