The command computes the topological Euler characteristic of the (smooth) projective variety V as an alternated sum of its Hodge numbers. The Hodge numbers can be computed directly using the command
hh.
A smooth plane quartic curve has genus 3 and topological Euler characteristic -4:
Quartic = Proj(QQ[x_0..x_2]/ideal(x_0^4+x_1^4+x_2^4)) |
euler(Quartic) |
The topological Euler characteristic of a smooth quintic hypersurface in projective fourspace is -200:
Quintic = Proj(QQ[x_0..x_4]/ideal(x_0^5+x_1^5+x_2^5+x_3^5+x_4^5-101*x_0*x_1*x_2*x_3*x_4)) |
euler(Quintic) |