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 |