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Real multiplication #266

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videlec opened this issue Oct 26, 2023 · 0 comments
Open

Real multiplication #266

videlec opened this issue Oct 26, 2023 · 0 comments
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@videlec
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videlec commented Oct 26, 2023 •
edited by saraedum
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Numerically check/guess whether a given surface belongs to a real multiplication locus.

  1. compute a basis of $\Omega(X)$ (using Add HarmonicDifferentials #213)
  2. compute periods $\int_\gamma \omega$ on the basis $\omega$ of $\Omega(X)$ and a basis $\gamma$ of $H_1(X; \mathbb{Z})$ and form the Riemann matrix
  3. use the same strategy as in sage code RiemannSurface.endomorphism_basis. The latter boils down to calling the standalone integer_matrix_relations.
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