CHOW GROUPS, CHOW COHOMOLOGY, AND LINEAR VARIETIES

By B. Totaro. Forum of Mathematics, Sigma, 2014

91 citations recorded by the source corpus.

Abstract We compute the Chow groups and the Fulton–MacPherson operational Chow cohomology ring for a class of singular rational varieties including toric varieties. The computation is closely related to the weight filtration on the ordinary cohomology of these varieties. We use the computation to answer one of the open problems about operational Chow cohomology: it does not have a natural map to ordinary cohomology.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/74812af7d7b680383daab5f7a6acf93ee527c059

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Sam Payne
2. David Anderson
3. B. Totaro
4. Kiumars Kaveh
5. Eric Katz
6. Claire Voisin
7. David Jensen
8. Walter Gubler

In Discrete Mathematics and Combinatorics

1. David Anderson
2. Sam Payne
3. B. Totaro
4. Eric Katz

In Geometry and Topology

1. David Anderson
2. Sam Payne
3. B. Totaro
4. Philipp Gross
5. Eric Katz
6. David Jensen
7. N. Perrin
8. Kiumars Kaveh

Citations in the corpus

• The motive of a classifying space (2014, background): “ubscheme Z, if Z and X − Z are linear schemes, then X is a linear scheme; and if X and Z are linear schemes, then X − Z is a linear scheme. (A slightly narrower class of linear schemes was studied in [54].) Some examples of linear schemes are all toric varieties, not necessarily smooth or compact, t”
• Operational K-Theory (2013, methodology): “As in Totaro’s analogous result for Chow cohomology [To1], Theorem 6.1 is an immediate consequence of two facts.”