First Milnor cohomology of hyperplane arrangements

被引：0

作者：

Budur, Nero ^{[1
]}

Dimca, Alexandru ^{[2
]}

Saito, Morihiko ^{[3
]}

机构：

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[2] Univ Nice Sophia Antipolis, UMR CNRS 6621, Lab JA Dieudonne, F-06108 Nice 02, France

[3] Kyoto Univ, RIMS, Kyoto 6068502, Japan

来源：

TOPOLOGY OF ALGEBRAIC VARIETIES AND SINGULARITIES | 2011年 / 538卷

关键词：

hyperplane arrangement; Milnor fiber; monodromy; multiplier ideal; MULTIPLIER IDEALS; LOCAL SYSTEMS; COMPLEMENTS; VARIETIES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show a combinatorial formula for a lower bound of the dimension of the non-unipotent monodromy part of the first Manor cohomology of a hyperplane arrangement satisfying some combinatorial conditions. This gives exactly its dimension if a stronger combinatorial condition is satisfied. We also prove a non-combinatorial formula for the dimension of the non-unipotent part of the first Milnor cohomology, which apparently depends on the position of the singular points. The latter generalizes a formula previously obtained by the second named author.

引用

页码：279 / +

页数：3

共 50 条

[1] On the Monodromy of Milnor Fibers of Hyperplane Arrangements
Bailet, Pauline
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2014, 57 (04): : 697 - 707
[2] Cohomology of the Milnor Fibre of a Hyperplane Arrangement with Symmetry
Dimca, Alexandru
Lehrer, Gus
CONFIGURATION SPACES: GEOMETRY, TOPOLOGY AND REPRESENTATION THEORY, 2016, 14 : 233 - 274
[3] Bernstein-Sato polynomial versus cohomology of the Milnor fiber for generic hyperplane arrangements
Walther, U
COMPOSITIO MATHEMATICA, 2005, 141 (01) : 121 - 145
[4] Morse theory, Milnor fibers and minimality of hyperplane arrangements
Randell, R
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (09) : 2737 - 2743
[5] Hyperplane Arrangements and Mixed Hodge Numbers of the Milnor Fiber
Kutler, Max
Usatine, Jeremy
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2022, 2022 (11) : 8644 - 8684
[6] Twisted cohomology of arrangements of lines and Milnor fibers
Salvetti, Mario
Serventi, Matteo
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2017, 17 (04) : 1461 - 1489
[7] Hyperplane arrangements, M-tame polynomials and twisted cohomology
Dimca, A
COMMUTATIVE ALGEBRA, SINGULARITIES AND COMPUTER ALGEBRA, 2003, 115 : 113 - 126
[8] On combinatorial invariance of the cohomology of the Milnor fiber of arrangements and the Catalan equation over function fields
Libgober, Anatoly
ARRANGEMENTS OF HYPERPLANES - SAPPORO 2009, 2012, 62 : 175 - 187
[9] Minimality of hyperplane arrangements and basis of local system cohomology
Yoshinaga, Masahiko
SINGULARITIES IN GEOMETRY AND TOPOLOGY: STRASBOURG 2009, 2012, 20 : 345 - 362
[10] On the monodromy action on Milnor fibers of graphic arrangements
Macinic, Anca Danielal
Papadima, Stefan
TOPOLOGY AND ITS APPLICATIONS, 2009, 156 (04) : 761 - 774

← 1 2 3 4 5 →