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...
| Authors: | , , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repository: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/425420 |
| Online Access: | 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: | Open access |
| Keyword: | Higgs bundle Hitchin map Moduli stack Torelli theorem |
| Summary: | 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 |
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