## Orbifold points on Teichmüller curves and Jacobians with complex multiplication

##### Author(s)

Mukamel, Ronen E. (Ronen Eliahu)
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##### Alternative title

Odbifold points and Jacobians with complex multiplication on Teichmüller curves in genus two

##### Other Contributors

Massachusetts Institute of Technology. Dept. of Mathematics.

##### Advisor

Curtis T. McMullen.

##### Terms of use

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Show full item record##### Abstract

For each integer D >/= 5 with D =/- 0 or 1 mod 4, the Weierstrass curve WD is an algebraic curve and a finite volume hyperbolic orbifold which admits an algebraic and isometric immersion into the moduli space of genus two Riemann surfaces. The Weierstrass curves are the main examples of Teichmüller curves in genus two. The primary goal of this thesis is to determine the number and type of orbifold points on each component of WD. Our enumeration of the orbifold points, together with [Ba] and [Mc3], completes the determination of the homeomorphism type of WD and gives a formula for the genus of its components. We use our formula to give bounds on the genus of WD and determine the Weierstrass curves of genus zero. We will also give several explicit descriptions of each surface labeled by an orbifold point on WD.

##### Description

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011. Cataloged from PDF version of thesis. Includes bibliographical references (p. 83-85).

##### Date issued

2011##### Department

Massachusetts Institute of Technology. Dept. of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.