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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.

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Computing basis of $\mathrm{Pic}(\bar{X})$ for a Del Pezzo surface

Say we are given a degree 2 del Pezzo $X$ given by $w^2=Q(x,y,z)$ where $Q(x,y,z)$ is degree 4. We can compute the exceptional lines by computing the 28 bitangent lines of $Q$ and look at the preimage …
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