MILNOR NUMBERS OF PROJECTIVE HYPERSURFACES WITH ISOLATED SINGULARITIES

被引：16

作者：

Huh, June ^{[1
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

DUKE MATHEMATICAL JOURNAL | 2014年 / 163卷 / 08期

基金：

美国国家科学基金会;

关键词：

POLAR CREMONA TRANSFORMATIONS; LEFSCHETZ THEOREMS; VARIETIES; TOPOLOGY;

D O I：

10.1215/00127094-2713700

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let V be a projective hypersurface of fixed degree and dimension which has only isolated singular points. We show that, if the sum of the Milnor numbers at the singular points of V is large, then V cannot have a point of large multiplicity, unless V is a cone. As an application, we give an affirmative answer to a conjecture of Dimca and Papadima.

引用

页码：1525 / 1548

页数：24

共 37 条

[1] MILNOR NUMBERS OF PROJECTIVE HYPERSURFACES AND THE CHROMATIC POLYNOMIAL OF GRAPHS
Huh, June
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 25 (03) : 907 - 927
[2] Results on Milnor Fibrations for Mixed Polynomials with Non-isolated Singularities
Grulha Jr, N. G.
Martins, R. S.
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2021, 52 (02): : 327 - 351
[3] THE BOUNDARY OF THE MILNOR FIBER FOR SOME NON-ISOLATED SINGULARITIES OF COMPLEX SURFACES
Michel, Francoise
Pichon, Anne
Weber, Claude
OSAKA JOURNAL OF MATHEMATICS, 2009, 46 (01) : 291 - 316
[4] Fibration theorems a la Milnor for analytic maps with non-isolated singularities
Cisneros-Molina, Jose Luis
Menegon, Aurelio
Seade, Jose
Snoussi, Jawad
SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2023, 18 (2): : 1 - 22
[5] Irregular surfaces on hypersurfaces of degree 4 with non-degenerate isolated singularities
Naie, Daniel
ADVANCES IN GEOMETRY, 2022, 22 (03) : 341 - 354
[6] Stability and Singularities of Relative Hypersurfaces
Angel Barja, Miguel
Stoppino, Lidia
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2016, 2016 (04) : 1026 - 1053
[7] The values of the Milnor genus on smooth projective connected complex varieties
Johnston, B
TOPOLOGY AND ITS APPLICATIONS, 2004, 138 (1-3) : 189 - 206
[8] Four-Dimensional Projective Orbifold Hypersurfaces
Brown, Gavin
Kasprzyk, Alexander
EXPERIMENTAL MATHEMATICS, 2016, 25 (02) : 176 - 193
[9] Hyperplane Arrangements and Mixed Hodge Numbers of the Milnor Fiber
Kutler, Max
Usatine, Jeremy
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2022, 2022 (11) : 8644 - 8684
[10] ON THE LIFTABILITY OF THE AUTOMORPHISM GROUP OF SMOOTH HYPERSURFACES OF THE PROJECTIVE SPACE
Gonzalez-Aguilera, Victor
Liendo, Alvaro
Montero, Pedro
ISRAEL JOURNAL OF MATHEMATICS, 2023, 255 (01) : 283 - 310

← 1 2 3 4 →