Torelli theorem for moduli stacks of vector bundles and principal G-bundles

Given any irreducible smooth complex projective curve X, of genus at least 2, consider the moduli stack of vector bundles on X of fixed rank and determinant. It is proved that the isomorphism class of the stack uniquely determines the isomorphism class of the curve X and the rank of the vector bundl...

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Detalles Bibliográficos
Autores: Alfaya, D., Biswas, I., Gómez, T.L., Mukhopadhyay, S.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/425420
Acceso en línea:http://hdl.handle.net/10261/425420
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85208130292&doi=10.1016%2Fj.geomphys.2024.105350&partnerID=40&md5=3bc4957b49ef76dd092406a2f871c03a
Access Level:acceso abierto
Palabra clave:Higgs bundle
Hitchin map
Moduli stack
Torelli theorem
Descripción
Sumario:Given any irreducible smooth complex projective curve X, of genus at least 2, consider the moduli stack of vector bundles on X of fixed rank and determinant. It is proved that the isomorphism class of the stack uniquely determines the isomorphism class of the curve X and the rank of the vector bundles. The case of trivial determinant, rank 2 and genus 2 is specially interesting: the curve can be recovered from the moduli stack, but not from the moduli space (since this moduli space is P3 thus independently of the curve). We also prove a Torelli theorem for moduli stacks of principal G-bundles on a curve of genus at least 3, where G is any non-abelian reductive group. © 2024 The Authors