Proof of Schubert's conjectures on double contacts.
| dc.contributor.author | Arrondo Esteban, Enrique | |
| dc.contributor.author | Mallavibarrena Martínez de Castro, Raquel | |
| dc.contributor.author | Sols Lucía, Ignacio | |
| dc.date.accessioned | 2023-06-20T18:41:53Z | |
| dc.date.available | 2023-06-20T18:41:53Z | |
| dc.date.issued | 1990 | |
| dc.description | Proceedings of the conference held in Sitges, June 1–6, 1987 | |
| dc.description.abstract | The purpose of the paper under review is to give a proof of six formulas by Schubert (two of which he proved and four of which he only conjectured) concerning the number of double contacts among the curves of two families of plane curves. The method consists in finding bases of the Chow groups of the Hilbert scheme of length 2 subschemes of the point- line incidence variety. This approach turns out to be much simpler than the one using the space of triangles as suggested by Schubert. As a byproduct, the authors obtain proofs of the classical formulas on triple contacts (i.e., single contacts of third order) between two such families of curves | |
| 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/20367 | |
| dc.identifier.doi | 10.1007/BFb0084039 | |
| dc.identifier.issn | 0075-8434 | |
| dc.identifier.officialurl | http://link.springer.com/chapter/10.1007%2FBFb0084039?LI=true | |
| dc.identifier.relatedurl | http://link.springer.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58341 | |
| dc.journal.title | Lecture notes in mathematics | |
| dc.page.final | 29 | |
| dc.page.initial | 1 | |
| dc.publisher | Springer | |
| dc.rights.accessRights | metadata only access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | flag variety | |
| dc.subject.keyword | number of double contacts | |
| dc.subject.keyword | families of plane curves | |
| dc.subject.keyword | Chow groups | |
| dc.subject.keyword | triple contacts | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | Proof of Schubert's conjectures on double contacts. | |
| dc.type | journal article | |
| dc.volume.number | 1436 | |
| dcterms.references | Bialynicki-Birula, A. Some properties of the descompositions of algebraic varieties determined by actions of a torus. Bulletin de l'Acad. Polonaise des Sciences. Série des sci. math. astr. et phys. Vol. 24, no 9 (1976), pp. 667–674. Byalynicki-Birula, A. Some theorems on actions of algebraic groups. Ann. of Math. Vol. 98. no 3 (1973) pp. 480–497. Elencwajg, G., Le Barz, P. Explicit computations in Hilb3ℙ2, in Algebraic Geometry. Sundance 1986 (A. Holme and R. Speiser eds.), Lect. Notes in Math. 1311,Springer-Verlag, pp. 76–100. Fulton, W. Intersection Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag (1984). Hartshorne, R. Algebraic Geometry, Springer-Verlag, GTM 52, 1977. Kleiman, S. The transversality of a general translate, Compositio Math. 38 (1974), 287–297. Mallavibarrena, R., Sols, I. Bases for the Chow groups of the Hilbert scheme of points in the plane. To appear in Compositio Math. Roberts, J.-Speiser, R. Enumerative Geometry of triangles, I, II, III. Comm. in Alg. 12(10) 1213–1255 (1984) Roberts, J.-Speiser, R. Enumerative Geometry of triangles, I, II, III. Comm. in Alg. 14(1), 155–191 (1986) 15(9), 1929–1966 (1987). Roberts, J.-Speiser, R. Enumerative Geometry of triangles, I, II, III. Comm. in Alg. 15(9), 1929–1966 (1987). Rosselló, F. Thesis, Univ. of Barcelona (forthcoming). Rosselló, F., Xambó, S. Computing Chow groups, in: Algebraic Geometry, Sundance 1986 (eds.: A. Holme and R. Speiser), Lect. Notes in Math. 1311, pp. 220–234. Schubert, H. Anzahlgeometrische Behandlung des Dreiecks. Math. Ann. 17 (1880) 153–212. Serre, J.P. Algèbre Locale. Multiplicités. LNM 11 (1965). | |
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