Topological invariants of isolated complete intersection curve singularities
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 975-987 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we present some formulae for topological invariants of projective complete intersection curves with isolated singularities in terms of the Milnor number, the Euler characteristic and the topological genus. We also present some conditions, involving the Milnor number and the degree of the curve, for the irreducibility of complete intersection curves.
In this paper we present some formulae for topological invariants of projective complete intersection curves with isolated singularities in terms of the Milnor number, the Euler characteristic and the topological genus. We also present some conditions, involving the Milnor number and the degree of the curve, for the irreducibility of complete intersection curves.
Classification : 32S50, 58K65
Keywords: topological invariants; genus; Euler characteristic; irreducibility criterion
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Pérez, V. H. Jorge; Hernandes, M. E. Topological invariants of isolated complete intersection curve singularities. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 975-987. http://geodesic.mathdoc.fr/item/CMJ_2009_59_4_a7/

[1] Arslan, F., Sertöz, S.: Genus calculations of complete intersections. Commun. Algebra 26 (1998), 2463-2471. | DOI | MR

[2] Buchweitz, R.-O., Greuel, G.-M.: Milnor number and deformation of complex curve singulaties. Invent. Math. 58 (1980), 241-281. | DOI | MR

[3] Dimca, A.: Singularities and Topology of Hypersurfaces. Universitext. Springer New York (1992). | MR

[4] Greuel, G. M.: Der Gauss-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten. Math. Ann. 214 (1975), 235-266 German. | DOI | MR | Zbl

[5] Harris, J.: On Severi problem. Invent. Math. 84 (1986), 445-461. | DOI | MR

[6] Hartshorne, R.: Algebraic Geometry. Graduate Texts in Mathematics 52. Springer New York-Heidelberg-Berlin (1977). | MR

[7] Hironaka, H.: On the arithmetic genera and the effective genera of algebraic curves. Mem. Coll. Sci., Univ. Kyoto, Ser. A 30 (1957), 177-195. | DOI | MR | Zbl

[8] Kleiman, S. L.: A generalized Teissier-Plücker formula. Contemp. Math. 162 (1994), 249-260. | DOI | MR | Zbl

[9] Kline, M.: Mathematical Thought from Ancient to Modern Times. Clarendon Press, Oxford Univ. Press New York (1990). | MR | Zbl

[10] Looijenga, E. J. N.: Isolated Singular Points on Complete Intersections. London Mathematical Society Lecture Note, Ser. 77. Cambridge University Press Cambridge (1984). | MR

[11] Mumford, D.: Algebraic Geometry. I: Complex Projective Varieties. Springer Berlin (1995). | MR | Zbl

[12] Severi, F.: Il Teorema di Riemann-Roch per curve, superficie e varietá. Ergebnisse der Math. Questioni Collegate. Springer Berlin-Göttingen-Heidelberg (1958), Italian. | MR