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== References == == References ==
*W. Fulton, R. MacPherson, F. Sottile, and B. Sturmfels, ‘Intersection theory on spherical varieties’, J. Alg. Geom. 4 (1995), 181–193. *W. Fulton, R. MacPherson, F. Sottile, and B. Sturmfels, ‘Intersection theory on spherical varieties’, J. Alg. Geom. 4 (1995), 181–193.
*Totaro, Chow groups, Chow cohomology and linear varieties. *Totaro,


{{geometry-stub}} {{geometry-stub}}

Revision as of 04:56, 4 November 2015

The basic question, still open as of, is whether there is a cycle map:

A ( X ) H ( X , Z ) . {\displaystyle A^{*}(X)\to \operatorname {H} ^{*}(X,\mathbb {Z} ).}

If X is smooth, such a map exists since A ( X ) {\displaystyle A^{*}(X)} is the usual Chow ring of X. (Totaro 2014) harv error: no target: CITEREFTotaro2014 (help) has shown that there might not be such a map even if X is a linear variety, roughly a variety admitting a cell decomposition.

References

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