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ToricVectorBundles :: eulerChi

eulerChi -- the Euler characteristic of a toric vector bundle

Synopsis

Description

This function computes the Euler characteristic of a vector bundle if only the bundle is given to the function. For this it first computes the set of all degrees that give non-zero cohomology (see deltaE) and then computes the Euler characteristic for each these degrees. If the underlying variety is not complete then this set may not be finite. Thus, for a non-complete toric variety an error is returned.

If in addition a one-column matrix over ZZ, representing a degree vector u, is given, it computes the Euler characteristic of the degree u-part of the vector bundle E. For this the variety need not be complete.

E = tangentBundle hirzebruchFan 3
u = matrix {{0},{0}}
eulerChi(u,E)
eulerChi E
E = tangentBundle(hirzebruchFan 3,"Type" => "Kaneyama")
u = matrix {{0},{0}}
eulerChi(u,E)
eulerChi E

See also

Ways to use eulerChi :