A smooth plane quartic curve has genus 3 and topological Euler characteristic -4:
i1 : Quartic = Proj(QQ[x_0..x_2]/ideal(x_0^4+x_1^4+x_2^4)) o1 = Quartic o1 : ProjectiveVariety |
i2 : euler(Quartic) o2 = -4 |
The topological Euler characteristic of a smooth quintic hypersurface in projective fourspace is -200:
i3 : 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)) o3 = Quintic o3 : ProjectiveVariety |
i4 : euler(Quintic) o4 = -200 |