{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/67810"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/67810","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Orbifold points on Teichmüller curves and Jacobians with complex multiplication","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Mukamel, Ronen E. (Ronen Eliahu)"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Curtis T. McMullen."],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011","date_published":"2011","updated_at":"2026-07-22T22:22:24Z","subjects":["Mathematics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/67810","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Curtis T. McMullen."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Dept. of Mathematics."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. Dept. of Mathematics."]},{"key":"dc:creator","label":"Author","values":["Mukamel, Ronen E. (Ronen Eliahu)"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2011-12-19T19:00:32Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2011-12-19T19:00:32Z"]},{"key":"dc:date.issued","label":"Date","values":["2011"]},{"key":"dc:publisher","label":"Institution","values":["Massachusetts Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/67810"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 83-85)."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Orbifold points on Teichmüller curves and Jacobians with complex multiplication"]}]}],"canonical_facts":{"dc:contributor.advisor":["Curtis T. McMullen."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:creator":["Mukamel, Ronen E. (Ronen Eliahu)"],"dc:date.accessioned":["2011-12-19T19:00:32Z"],"dc:date.available":["2011-12-19T19:00:32Z"],"dc:date.issued":["2011"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 83-85)."],"dc:description.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."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/67810"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["Orbifold points on Teichmüller curves and Jacobians with complex multiplication"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:22:24Z"}