genus(ProjectiveVariety)

Synopsis

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