chern (i, F)
The total Chern class of a coherent sheaf F on a variety X is defined axiomatically by an element chern F in the Chow ring of X such that the following three conditions hold:
The i-th component of chern F is chern (i, F), so we obtain chern F == chern (0, F) + chern (1, F) + ... + chern (dim X, F).
The total Chern class for the tangent bundle on projective space is particularly simple; the coefficient of i-th component is a binomial coefficient.
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On a complete smooth normal toric variety, the total Chern class of the cotangent sheaf is a product over the torus-invariant divisors of the total Chern classes of the inverse of the corresponding line bundles.
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The source of this document is in NormalToricVarieties/ChowDocumentation.m2:337:0.