Title:
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Topological invariants of isolated complete intersection curve singularities (English) |
Author:
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Pérez, V. H. Jorge |
Author:
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Hernandes, M. E. |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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59 |
Issue:
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4 |
Year:
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2009 |
Pages:
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975-987 |
Summary lang:
|
English |
. |
Category:
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math |
. |
Summary:
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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. (English) |
Keyword:
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topological invariants |
Keyword:
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genus |
Keyword:
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Euler characteristic |
Keyword:
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irreducibility criterion |
MSC:
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32S50 |
MSC:
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58K65 |
idZBL:
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Zbl 1224.32024 |
idMR:
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MR2563570 |
. |
Date available:
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2010-07-20T15:51:50Z |
Last updated:
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2020-07-03 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/140529 |
. |
Reference:
|
[1] Arslan, F., Sertöz, S.: Genus calculations of complete intersections.Commun. Algebra 26 (1998), 2463-2471. MR 1627868, 10.1080/00927879808826291 |
Reference:
|
[2] Buchweitz, R.-O., Greuel, G.-M.: Milnor number and deformation of complex curve singulaties.Invent. Math. 58 (1980), 241-281. MR 0571575, 10.1007/BF01390254 |
Reference:
|
[3] Dimca, A.: Singularities and Topology of Hypersurfaces. Universitext.Springer New York (1992). MR 1194180 |
Reference:
|
[4] Greuel, G. M.: Der Gauss-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten.Math. Ann. 214 (1975), 235-266 German. Zbl 0285.14002, MR 0396554, 10.1007/BF01352108 |
Reference:
|
[5] Harris, J.: On Severi problem.Invent. Math. 84 (1986), 445-461. MR 0837522, 10.1007/BF01388741 |
Reference:
|
[6] Hartshorne, R.: Algebraic Geometry. Graduate Texts in Mathematics 52.Springer New York-Heidelberg-Berlin (1977). MR 0463157 |
Reference:
|
[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. Zbl 0099.15702, MR 0090850, 10.1215/kjm/1250777055 |
Reference:
|
[8] Kleiman, S. L.: A generalized Teissier-Plücker formula.Contemp. Math. 162 (1994), 249-260. Zbl 0820.14039, MR 1272702, 10.1090/conm/162/01536 |
Reference:
|
[9] Kline, M.: Mathematical Thought from Ancient to Modern Times.Clarendon Press, Oxford Univ. Press New York (1990). Zbl 0864.01001, MR 0472307 |
Reference:
|
[10] Looijenga, E. J. N.: Isolated Singular Points on Complete Intersections. London Mathematical Society Lecture Note, Ser. 77.Cambridge University Press Cambridge (1984). MR 0747303 |
Reference:
|
[11] Mumford, D.: Algebraic Geometry. I: Complex Projective Varieties.Springer Berlin (1995). Zbl 0821.14001, MR 1344216 |
Reference:
|
[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 0094357 |
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