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May 2021 The Bolza Curve and Some Orbifold Ball Quotient Surfaces
Vincent Koziarz, Carlos Rito, Xavier Roulleau
Michigan Math. J. 70(2): 423-448 (May 2021). DOI: 10.1307/mmj/1595405184

Abstract

We study Deraux’s nonarithmetic 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 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 that provides the above-mentioned ball quotient orbifold surfaces.

Citation

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Vincent Koziarz. Carlos Rito. Xavier Roulleau. "The Bolza Curve and Some Orbifold Ball Quotient Surfaces." Michigan Math. J. 70 (2) 423 - 448, May 2021. https://doi.org/10.1307/mmj/1595405184

Information

Received: 30 April 2019; Revised: 14 February 2020; Published: May 2021
First available in Project Euclid: 22 July 2020

Digital Object Identifier: 10.1307/mmj/1595405184

Subjects:
Primary: 22E40
Secondary: 14J26, 14L30, 20H15

Rights: Copyright © 2021 The University of Michigan

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Vol.70 • No. 2 • May 2021
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