KOZIARZ, Vincent; RITO, Carlos; ROULLEAU, Xavier

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KOZIARZ, Vincent
Institut de Mathématiques de Bordeaux [IMB]

RITO, Carlos
Universidade de Trás-os-Montes e Alto Douro [UTAD]

ROULLEAU, Xavier
Institut de Mathématiques de Marseille [I2M]

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Michigan Mathematical Journal. 2021

University of Michigan

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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.< Réduire

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The Bolza curve and some orbifold ball quotient surfaces

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