On Chow Rings of Fine Moduli Spaces of Modules

Details On Chow Rings of Fine Moduli Spaces of Modules On Chow Rings of Fine Moduli Spaces of Modules

1994-03-18

arxiv.org/abs/alg-geom/9403014v1

J. reine angew. Math. 461 (1995), 179-187

Mathematics

Algebraic Geometry

8 pages, LATeX

Scientific paper

Let $M$ be a complete nonsingular fine moduli space of modules over an algebra $S$. A set of conditions is given for the Chow ring of $M$ to be generated by the Chern classes of certain universal bundles occurring in a projective resolution of the universal $S$-module on $M$. This result is then applied to the varieties $G_T$ parametrizing homogeneous ideals of $k[x,y]$ of Hilbert function $T$, to moduli spaces of representations of quivers, and finally to moduli spaces of sheaves on ${\Bbb P}^2$, reinterpreting a result of Ellingsrud and Str\o mme.

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