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On smooth plane models for modular curves of Shimura type
Multi angle
Authors : Lorenzo Garcia, Elisa (Author of the conference)
CIRM (Publisher )
11F11 - Holomorphic modular forms of integral weight
11G18 - Arithmetic aspects of modular and Shimura varieties
14G35 - Modular and Shimura varieties
14H45 - Special curves and curves of low genus
CIRM (Publisher )
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Abstract :
In this talk we will see that there are only finitely many modular curves that admit a smooth plane model. Moreover, if the degree of the model is greater than or equal to 19, no such curve exists. For modular curves of Shimura type we will show that none can admit a smooth plane model of degree 5, 6 or 7. Further, if a modular curve of Shimura type admits a smooth plane model of degree 8 we will see that it must be a twist of one of four curves.
This is joint work with Samuele Anni and Eran Assaf.
Keywords : modular curves; congruence subgroups; cusp forms; canonical model
MSC Codes : This is joint work with Samuele Anni and Eran Assaf.
Keywords : modular curves; congruence subgroups; cusp forms; canonical model
11F11 - Holomorphic modular forms of integral weight
11G18 - Arithmetic aspects of modular and Shimura varieties
14G35 - Modular and Shimura varieties
14H45 - Special curves and curves of low genus
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Information on the Video
Film maker : Petit, JeanLanguage : English Available date : 13/03/2023 Conference Date : 27/02/2023 Subseries : Research talks arXiv category : Number Theory ; Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:00:50 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-02-27_Lorenzo-Garcia.mp4 
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Information on the Event
Event Title : COUNT - Computations and their Uses in Number Theory / Les calculs et leurs utilisations en théorie des nombresEvent Organizers : Anni, Samuele ; Allombert, Bill ; Balakrishnan, Jennifer ; Bruin, Peter ; Kilicer, Pinar ; Streng, Marco Dates : 27/02/2023 - 03/03/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2805.html
Citation Data
DOI : 10.24350/CIRM.V.20007003Cite this video as: Lorenzo Garcia, Elisa (2023). On smooth plane models for modular curves of Shimura type. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20007003 URI : http://dx.doi.org/10.24350/CIRM.V.20007003 |
See Also
- [Multi angle] Modular curves and finite groups: building connections via computation / Author of the conference Roe, David.
- [Multi angle] Endomorphism algebras of geometrically split abelian surfaces over Q / Author of the conference Guitart, Xavier.
- [Multi angle] Endomorphism algebras of geometrically split genus 2 jacobians over Q / Author of the conference Fité, Francesc.
- [Multi angle] Minimal torsion curves in geometric isogeny classes / Author of the conference Bourdon, Abbey.
Bibliography
- ANNI, Samuele, ASSAF, Eran, et GARCÍA, Elisa Lorenzo. On smooth plane models for modular curves of Shimura type. arXiv preprint arXiv:2203.06370, 2022. - https://doi.org/10.48550/arXiv.2203.06370
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