# Tag Info

## New answers tagged algebraic-curves

8

Let $C$ be the union of 5 lines in general position in $\mathbb{P}^2$ (hence with 10 pairwise intersection points $P_{ij}$, $1 \le i < j \le 5$) and let $F$ be the equation of $C$. We have the standard exact sequence $$0 \to \mathcal{O}_C(-5) \stackrel{dF}\to \Omega_{\mathbb{P}^2}\vert_C \to \Omega_C \to 0.$$ Taking its dual we obtain an exact sequence $... 1 Interestingly, I only found the Klein quartic$K = x^3y + y^3z + z^3x$and the Fermat curve$F = x^7 + y^7 + z^7$. Both of them cover (at least over$\overline{\mathbb{Q}}$) the elliptic curve of$j$-invariant$-3^3 5^3$with complex multiplication by$\mathbb{Z}[(1 + \sqrt{-7})/2]$. As is known,$F$covers$K$and$K\$ is birationally isomorphic to the ...

Top 50 recent answers are included