A Divisibility Theorem for the Alexander Polynomial of a Plane Algebraic Curve

被引：0

作者：

A. I. Degtyarev

机构：

[1] Bilkent University,

来源：

Journal of Mathematical Sciences | 2004年 / 119卷 / 2期

关键词：

Singular Point; Algebraic Curve; Alexander Polynomial; Local Polynomial; Plane Algebraic;

D O I：

10.1023/B:JOTH.0000008758.55140.e7

中图分类号：

学科分类号：

摘要：

An upper estimate for the Alexander polynomial of an algebraic curve is obtained, which sharpens Libgober's estimate in terms of the local polynomials at the singular points of the curve: only those singular points may contribute to the Alexander polynomial of the curve that are in the excess of the hypothesis of Nori's vanishing theorem. Bibliography: 19 titles.

引用

页码：205 / 210

页数：5

共 50 条

[1] AN ALGEBRAIC COMPUTATION OF THE ALEXANDER POLYNOMIAL OF A PLANE ALGEBRAIC CURVE
KOHNO, T
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1983, 59 (03) : 94 - 97
[2] The Alexander polynomial of a plane curve singularity via the ring of functions on IT
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[J]. DUKE MATHEMATICAL JOURNAL, 2003, 117 (01) : 125 - 156
[3] The Alexander polynomial of plane curve singularities and rings of functions on curves
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Delgado, F
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[J]. RUSSIAN MATHEMATICAL SURVEYS, 1999, 54 (03) : 634 - 635
[4] ALEXANDER POLYNOMIAL OF PLANE ALGEBRAIC-CURVES AND CYCLIC MULTIPLE PLANES
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[J]. DUKE MATHEMATICAL JOURNAL, 1982, 49 (04) : 833 - 851
[5] The Alexander polynomial of a plane curve singularity and integrals with respect to the Euler characteristic
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[J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 2003, 14 (01) : 47 - 54
[6] A Symbolic-Numeric Algorithm for Computing the Alexander Polynomial of a Plane Curve Singularity
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[7] ON THE ALEXANDER POLYNOMIAL OF ALTERNATING ALGEBRAIC KNOTS
MURASUGI, K
[J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1985, 39 (DEC): : 317 - 333
[8] Integration with respect to the Euler characteristic over a function space and the Alexander polynomial of a plane curve singularity
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[J]. RUSSIAN MATHEMATICAL SURVEYS, 2000, 55 (06) : 1148 - 1149
[9] ALEXANDER INVARIANTS OF PLANE ALGEBRAIC-CURVES
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[J]. PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS, 1983, 40 : 135 - 143
[10] ALEXANDER POLYNOMIALS OF PLANE ALGEBRAIC-CURVES
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[J]. RUSSIAN ACADEMY OF SCIENCES IZVESTIYA MATHEMATICS, 1994, 42 (01): : 67 - 89

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