Misplaced Pages

This is an old revision of this page, as edited by TakuyaMurata (talk | contribs) at 04:59, 4 November 2015. The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

The basic question was whether there is a cycle map:

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

If X is smooth, such a map exists since ${\displaystyle A^{*}(X)}$ 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

• 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

This geometry-related article is a stub. You can help Misplaced Pages by expanding it.

• v
• t
• e