Stability of conic bundles - (With an appendix by Mundet I Riera)
| dc.contributor.author | Sols Lucía, Ignacio | |
| dc.contributor.author | Gómez, Tomás L. | |
| dc.date.accessioned | 2023-06-20T18:42:03Z | |
| dc.date.available | 2023-06-20T18:42:03Z | |
| dc.date.issued | 2000-11 | |
| dc.description.abstract | Roughly speaking, a conic bundle is a surface, fibered over a curve, such that the fibers are conics (not necessarily smooth). We define stability for conic bundles and construct a moduli space. We prove that (after fixing some invariants) these moduli spaces are irreducible (under some conditions). Conic bundles can be thought of as generalizations of orthogonal bundles on curves. We show that in this particular case our definition of stability agrees with the definition of stability for orthogonal bundles. Finally, in an appendix by I. Mundet i Riera, a Hitchin-Kobayashi correspondence is stated for conic bundles. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/20448 | |
| dc.identifier.doi | 10.1142/S0129167X00000507 | |
| dc.identifier.issn | 0129-167X | |
| dc.identifier.officialurl | http://www.worldscientific.com/doi/pdf/10.1142/S0129167X00000507 | |
| dc.identifier.relatedurl | http://www.worldscientific.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58349 | |
| dc.issue.number | 8 | |
| dc.journal.title | International journal of mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 1055 | |
| dc.page.initial | 1027 | |
| dc.publisher | World Scientific | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 512 | |
| dc.subject.keyword | Principal bundles | |
| dc.subject.keyword | Algebraic-curves | |
| dc.subject.keyword | Moduli | |
| dc.subject.ucm | Álgebra | |
| dc.subject.unesco | 1201 Álgebra | |
| dc.title | Stability of conic bundles - (With an appendix by Mundet I Riera) | |
| dc.type | journal article | |
| dc.volume.number | 11 | |
| dcterms.references | D. Huybrechts and M. Lehn, Framed modules and their moduli, Int. J.Math. 6 (1995), 297-324. D. Huybrechts and M. Lehn, The geometry of moduli spaces of sheaves, Aspects of Mathematics E31, Vieweg, Braunschweig/Wiesbaden, 1997. A. D. King and P. E. Newstead, Moduli of Brill-Noether pairs on algebraic curves, Int. J. Math. 6 (1995), 733-748. D. Luna, Slices étales, Bull. Soc. Math. France, Mémoire 33 (1973), 81-105. I. Mundet i Riera, A Hitchin-Kobayashi correspondence for Kaehler fibrations, math.DG/9901076 J. Murre, Lectures on an Introduction to Grothendieck's Theory of the Fundamental Group, Lecture Notes, Tata Institute of Fundamental Research, Bombay, 1967. S. Ramanan, Orthogonal and spin bundles over hyperelliptic curves, Proc. Indian Acad. Sci., Math. Sci. 90 (1981), 151-166. A. Ramanathan, Stable principal bundles on a compact Riemann surface, Math. Ann. 213 (1975), 129-152. A. Ramanathan, Moduli for principal bundles over algebraic curves: I and II, Proc. Indian Acad. Sci., Math. Sci. 106 (1996), 301-328 and 421-449. C. Simpson, Moduli of representations of the fundamental group of a smooth projective variety I, Publ. Math. I.H.E.S. 79 (1994), 47-129 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 6d35def4-3d5f-4978-800f-82b7edf76b5d | |
| relation.isAuthorOfPublication.latestForDiscovery | 6d35def4-3d5f-4978-800f-82b7edf76b5d |
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