On sextic curves with big Milnor number.
| dc.book.title | Trends in Singularities | |
| dc.contributor.author | Artal Bartolo, Enrique | |
| dc.contributor.author | Carmona Ruber, Jorge | |
| dc.contributor.author | Cogolludo Agustín, José Ignacio | |
| dc.contributor.editor | Libgober, Amatoly | |
| dc.contributor.editor | Tibăr, Mihai | |
| dc.date.accessioned | 2023-06-20T21:07:42Z | |
| dc.date.available | 2023-06-20T21:07:42Z | |
| dc.date.issued | 2002 | |
| dc.description.abstract | In this work we present an exhaustive description, up to projective isomorphism, of all irreducible sextic curves in ℙ2 having a singular point of type , A n ,n⩾15 n ≥ 15, only rational singularities and global Milnor number at least 18. Moreover, we develop a method for an explicit construction of sextic curves with at least eight — possibly infinitely near — double points. This method allows us to express such sextic curves in terms of arrangements of curves with lower degrees and it provides a geometric picture of possible deformations. Because of the large number of cases, we have chosen to carry out only a few to give some insights into the general situation. | |
| dc.description.department | Sección Deptal. de Sistemas Informáticos y Computación | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGES | |
| dc.description.sponsorship | DGES | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/22480 | |
| dc.identifier.doi | 10.1007/978-3-0348-8161-6_1 | |
| dc.identifier.isbn | 978-3-0348-9461-6 | |
| dc.identifier.officialurl | http://link.springer.com/chapter/10.1007/978-3-0348-8161-6_1 | |
| dc.identifier.relatedurl | http://link.springer.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/60756 | |
| dc.language.iso | eng | |
| dc.page.final | 29 | |
| dc.page.initial | 1 | |
| dc.page.total | 246 | |
| dc.publication.place | USA | |
| dc.publisher | Birkhäuser Basel | |
| dc.relation.projectID | PB97-0284-C02-02 | |
| dc.relation.projectID | PB97-0284-C02-01 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | Equisingular family | |
| dc.subject.keyword | Sextic curves | |
| dc.subject.keyword | Deformation | |
| dc.subject.keyword | Fundamental group | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | On sextic curves with big Milnor number. | |
| dc.type | book part | |
| dcterms.references | 1.E. Artal Bartolo, Sur les couples de Zariski, J.Algebraic Geom. 3 (1994), no. 2, 223–247. E. Artal Bartolo, J. Carmona, J.I. Cogolludo, and H.Tokunaga, On curves with singular points in special position, J. Knot Theory Ramifications 10 (2001), no. 4,547–578. A. I. Degtyarëv, Alexander polynomial of a curve of degree six, J. Knot Theory Ramifications 3 (1994), no. 4, 439–454. A. Dimca, Singularities and topology of hypersurfaces, Universitext, Springer-Verlag, New York, 1992. K. Kodaira, On the structure of compact complex analytic surfaces. II, Amer. J. Math. 88 (1966), 682–721. A. Libgober, Alexander polynomial of plane algebraic curves and cyclic multiple planes, Duke Math. J. 49 (1982), no. 4, 833–851. I. Luengo, On the existence of complete families of projective plane curves, which are obstructed, J. London Math. Soc. (2) 36 (1987), no. 1, 33–43. S. Yu. Orevkov and E. I. Shustin, Flexible - algebraically unrealizable curves: rehabilitation of Hilbert-Rohn-Gudkov approach, Preprint, 2000. D.T. Pho, Classification of singularities on torus curves of type (2, 3), to appear in Kodai Math. J., 2001. D.T. Pho and M. Oka, Fundamental group of sextics of torus type, this Volume. T. Shioda, On the Mordell-Weil lattices,Comment. Math.Univ. St. Paul. 39 (1990), no. 2, 211–240. H. Tokunaga, Some examples of Zariski pairs arising from certain elliptic K3 surfaces. II. Degtyarev’s conjecture,Math. Z. 230 (1999), no. 2, 389–400. J.-G. Yang, Sextic curves with simple singularities,Tohoku Math. J. (2) 48 (1996), no. 2, 203–227. H. Yoshihara, On plane rational curves, Proc. Japan Acad. Ser. A Math. Sci. 55 (1979), no. 4, 152–155. O. Zariski, On the problem of existence of algebraic functions of two variables possessing a given branch curve,Amer. J. Math. 51 (1929), 305–328. O. Zariski, On the irregularity of cyclic multiple planes, Ann. Math. 32 (1931), 445–489. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | faea3c31-07a3-433c-96f8-f1bfae9110a1 | |
| relation.isAuthorOfPublication.latestForDiscovery | faea3c31-07a3-433c-96f8-f1bfae9110a1 |
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