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Article Dans Une Revue Michigan Mathematical Journal Année : 2021

The Bolza curve and some orbifold ball quotient surfaces

Résumé

We study Deraux's non arithmetic orbifold ball quotient surfaces obtained as birational transformations of a quotient $X$ of a particular Abelian surface $A$. Using the fact that $A$ is the Jacobian of the Bolza genus $2$ curve, we identify $X$ as the weighted projective plane $\mathbb{P}(1,3,8)$. We compute the equation of the mirror $M$ of the orbifold ball quotient $(X,M)$ and by taking the quotient by an involution, we obtain an orbifold ball quotient surface with mirror birational to an interesting configuration of plane curves of degrees $1,2$ and $3$. We also exhibit an arrangement of four conics in the plane which provides the above-mentioned ball quotient orbifold surfaces.
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Dates et versions

hal-02112689 , version 1 (12-07-2024)

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Vincent Jf Koziarz, Carlos Rito, Xavier Roulleau. The Bolza curve and some orbifold ball quotient surfaces. Michigan Mathematical Journal, 2021, 70 (2), ⟨10.1307/mmj/1595405184⟩. ⟨hal-02112689⟩
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