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Macaulay2Doc :: genus(ProjectiveVariety)

genus(ProjectiveVariety) -- arithmetic genus

Synopsis

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

See also