# genus(ProjectiveVariety) -- arithmetic genus

## Synopsis

• Function: genus
• Usage:
genus V
• Inputs:
• Outputs:

## Description

Computes the arithmetic genus of the projective scheme VA nodal plane cubic curve has arithmetic genus 1:
 i1 : V = Proj(QQ[a,b,c]/ideal(b^2*c-a^2*(a+c))) o1 = V o1 : ProjectiveVariety i2 : genus V o2 = 1
The Fano model of a Reye type Enriques surface in projective fivespace:
 i3 : R = ZZ/101[x_0..x_5]; i4 : M = random(R^4, R^{4:-1}); 4 4 o4 : Matrix R <--- R i5 : I = minors(3, M+transpose(M)); o5 : Ideal of R i6 : V = Proj(R/I); i7 : genus V o7 = 0