On the rational homotopy type of a moduli space of vector bundles over a curve
| dc.contributor.author | Biswas, Indrani | |
| dc.contributor.author | Muñoz, Vicente | |
| dc.date.accessioned | 2023-06-20T09:41:47Z | |
| dc.date.available | 2023-06-20T09:41:47Z | |
| dc.date.issued | 2008 | |
| dc.description.abstract | We study the rational homotopy of the moduli space N-X that parametrizes the isomorphism classes of all stable vector bundles of rank two and fixed determinant of odd degree over a compact connected Riemann surface X of genus g, with g >= 2. The symplectic group Aut(H-1(X, Z)) congruent to Sp(2g, Z) has a natural action on the rational homotopy groups pi(n)(N-X)circle times(Z)Q. We prove that this action extends to an action of Sp(2g, C) on pi(n)(N-X)circle times C-Z. We also show that pi(n)(N-X)circle times C-Z is a non-trivial representation of Sp(2g, C) congruent to Aut (H-1(X, C)) for all n >= 2g - 1. In particular, N-X is a rationally hyperbolic space. In the special case where g = 2, for each n is an element of N, we compute the leading Sp(2g, C) representation occurring in pi(n)(N-X)circle times C-Z. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MCyT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17141 | |
| dc.identifier.issn | 1019-8385 | |
| dc.identifier.officialurl | http://www.intlpress.com/CAG/ | |
| dc.identifier.relatedurl | http://www.intlpress.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50200 | |
| dc.issue.number | 1 | |
| dc.journal.title | Communications in Analysis and Geometry | |
| dc.language.iso | eng | |
| dc.page.final | 215 | |
| dc.page.initial | 183 | |
| dc.publisher | Int press co ltd | |
| dc.relation.projectID | MTM2004-07090-C03-01. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.cdu | 514 | |
| dc.subject.keyword | Vector bundles | |
| dc.subject.keyword | Moduli space | |
| dc.subject.keyword | Smooth projective curve | |
| dc.subject.keyword | Riemann surface | |
| dc.subject.keyword | Rational homotopy groups | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | On the rational homotopy type of a moduli space of vector bundles over a curve | |
| dc.type | journal article | |
| dc.volume.number | 15 | |
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| dspace.entity.type | Publication |
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