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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 ...


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