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genera(CoherentSheaf) -- list of the successive linear sectional arithmetic genera

Synopsis

Usage:
genera M
Function: genera
Inputs:
- M, a coherent sheaf
Outputs:
- a list, of the successive linear sectional arithmetic genera of the succesive generic hyperplane restrictions of M

Description

Computes the list of succesive generic linear sectional arithmetic genera, where the i-th entry in the list is (-1)^dim-support -i * (chi(M ** OO_lin-section) - 1)).

i1 : V = Proj(ZZ/101[x_0..x_2]);

i2 : M = sheaf(image matrix {{x_0^3+x_1^3+x_2^3}})

o2 = image | x_0^3+x_1^3+x_2^3 |

                                         1
o2 : coherent sheaf on V, subsheaf of OO
                                        V

i3 : genera M

o3 = {0, 3, 0}

o3 : List

See also

euler -- Euler characteristic