The Schubert triangle geometry on an algebraic surface
| dc.contributor.author | Sols Lucía, Ignacio | |
| dc.contributor.author | Hermoso, Carlos | |
| dc.date.accessioned | 2023-06-20T10:33:48Z | |
| dc.date.available | 2023-06-20T10:33:48Z | |
| dc.date.issued | 2006 | |
| dc.description.abstract | For a smooth complex projective surface, and for two families of curves with traditional singularities in it, we enumerate the pairs of curves in each family having two points of contact among them, thus generalizing the double contact formulae known or conjectured by Zeuthen and Schubert in the case of the complex projective plane. The technique we use to this purpose is a particular notion of triangle which can he defined in any smooth surface, thus potentially generalizing to arbitrary surfaces the Schubert technique of triangles. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Spanish Ministry of Education and Science | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/20496 | |
| dc.identifier.doi | 10.1080/00927870600936799 | |
| dc.identifier.issn | 0092-7872 | |
| dc.identifier.officialurl | http://www.tandfonline.com/doi/pdf/10.1080/00927870600936799 | |
| dc.identifier.relatedurl | http://www.tandfonline.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50530 | |
| dc.issue.number | 12 | |
| dc.journal.title | Communications in Algebra | |
| dc.language.iso | eng | |
| dc.page.final | 4621 | |
| dc.page.initial | 4597 | |
| dc.publisher | Taylor & Francis | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512 | |
| dc.subject.keyword | Algebraic surfaces | |
| dc.subject.keyword | Intersection theory | |
| dc.subject.keyword | Schubert triangles | |
| dc.subject.ucm | Álgebra | |
| dc.subject.unesco | 1201 Álgebra | |
| dc.title | The Schubert triangle geometry on an algebraic surface | |
| dc.type | journal article | |
| dc.volume.number | 34 | |
| dcterms.references | Arrondo, E., Mallavibarrena, R., Sols, I. (1990). Proof of the Schubert's conjectures on double contacts. In: Xambo-Descamps, S., ed. Enumerative Geometry. Lecture Notes in Math. Vol. 1436. Springer, pp. 1–29. Arrondo, E., Speiser, R., Sols, I. (1997). Global moduli for contacts. Ark. Mat. 35(1):1–57. Fantechi, B., Göttsche, L. (1993). The cohomology ring of the Hilbert scheme of 3 points on a smooth projective variety. J. Reine Angew. Math. 439:147–158. Fulton, W. (1984). Intersection Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3 Folge, Band 2. Berlin-New York: Springer-Verlag. Griffiths, P., Harris, J. (1978). Principles of Algebraic Geometry. Pure and Applied Mathematics. J. Wiley & Sons, Inc. Wiley Classics Library. Hartshorne, R. (1977). Algebraic Geometry. Graduate Texts in Math 52. New York-Heidelberg: Springer-Verlag. Hermoso, C. (2006). Geometría Enumerativa en una Superficie Algebraica. Ph. D. thesis. Universidad Complutense de Madrid. Available in www.ucm.es/BUCM/2006.htm. Hermoso, C., Sols, I. (1996). Bases of the homology spaces of the Hilbert scheme of points in an algebraic surface. Revista Matemática de la U.C.M. 9(1):53–66. Kleiman, S. L. (1973). Transversality of the general translate. Compo. Math. 28:287–297. Le Barz, P. (1987). Quelques calculs dans la varieté des alignements. Advances in Mathematics 64(2):87–117. Schubert, H. (1880). Anzahlgeometrische Behandlung des Dreiecks. Math.Ann. 17:153–212. Speiser, R. (1986). Transversality Theorems for Families of Maps. Lecture Notes in Math. 1311. Springer, pp. 235–252. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 6d35def4-3d5f-4978-800f-82b7edf76b5d | |
| relation.isAuthorOfPublication.latestForDiscovery | 6d35def4-3d5f-4978-800f-82b7edf76b5d |
Download
Original bundle
1 - 1 of 1