# genera(ProjectiveVariety) -- list of the successive linear sectional arithmetic genera

## Synopsis

• Function: genera
• Usage:
genera V
• Inputs:
• Outputs:
• a list, of the successive linear sectional arithmetic genera of V

## Description

Computes the list of successive linear sectional arithmetic genera, where the i-th entry in the list is the arithmetic genus of the i-th successive generic hyperplane section of V (= (-1)^dim-lin-section * (chi(OO_lin-section) - 1)).

A complete intersection of type (2,3) in projective fourspace; its hyperplane section is a canonical curve of genus 4:

 i1 : R = ZZ/101[x_0..x_4]; i2 : V = Proj(R/(ideal random(R^1, R^{-2,-3}))); i3 : genera V o3 = {1, 4, 5} o3 : List