On the generalized Nash problem for smooth germs and adjacencies of curve singularities

被引：1

作者：

Fernandez de Bobadilla, Javier ^{[1
,2
]}

Pe Pereira, Maria ^{[3
]}

Popescu-Pampu, Patrick ^{[4
]}

机构：

[1] Basque Fdn Sci, Ikerbasque, Maria Diaz de Haro 3, Bilbao 48013, Bizkaia, Spain

[2] BCAM, Mazarredo 14, E-48009 Bilbao, Basque Country, Spain

[3] UAM, Inst Ciencias Matemat ICMAT, Nicolas Cabrera 13-15,Campus Cantoblanco, Madrid 28049, Spain

[4] Univ Lille 1, UFR Maths, Batiment M2, F-59655 Villeneuve Dascq, France

来源：

ADVANCES IN MATHEMATICS | 2017年 / 320卷

基金：

欧洲研究理事会;

关键词：

Adjacency of singularities; Approximate roots; Arc spaces; Maximal divisorial set; Nash problem; Plane curve singularities; SURFACE SINGULARITIES; ARCS; MAP; FAMILIES; SPACES;

D O I：

10.1016/j.aim.2017.09.035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we explore the generalized Nash problem for arcs on a germ of smooth surface: given two prime divisors above its special point, to determine whether the arc space of one of them is included in the arc space of the other one. We prove that this problem is combinatorial and we explore its relation with several notions of adjacency of plane curve singularities. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：1269 / 1317

页数：49

共 50 条

[1] Determinacy of smooth germs with real isolated line singularities
Sun, BH
Wilson, LC
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (09) : 2789 - 2797
[2] Nash problem for surface singularities is a topological problem
Fernandez de Bobadilla, Javier
[J]. ADVANCES IN MATHEMATICS, 2012, 230 (01) : 131 - 176
[3] The Minimal Tjurina Number of Irreducible Germs of Plane Curve Singularities
Alberich-Carraminana, Maria
Almiron, Patricio
Blanco, Guillem
Melle-Hernandez, Alejandro
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2021, 70 (04) : 1211 - 1220
[4] The Nash problem on arc families of singularities
Ishii, S
Kollár, J
[J]. DUKE MATHEMATICAL JOURNAL, 2003, 120 (03) : 601 - 620
[5] Nash problem for quotient surface singularities
Pereira, Maria Pe
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2013, 87 : 177 - 203
[6] TORSION PROBLEM IN CURVE SINGULARITIES
GUTTES, K
[J]. ARCHIV DER MATHEMATIK, 1990, 54 (05) : 499 - 510
[7] On a problem concerning the ring of Nash germs and the Borel mapping
Berraho, Mourad
[J]. AIMS MATHEMATICS, 2020, 5 (02): : 923 - 929
[8] Algebraization of analytic curve germs passing through isolated surface singularities
Manetti, M
[J]. ARCHIV DER MATHEMATIK, 1996, 66 (05) : 428 - 440
[9] The local Nash problem on arc families of singularities
Ishii, Shihoko
[J]. ANNALES DE L INSTITUT FOURIER, 2006, 56 (04) : 1207 - 1224
[10] Polar germs, Jacobian ideal and analytic classification of irreducible plane curve singularities
Casas-Alvero, Eduardo
[J]. MANUSCRIPTA MATHEMATICA, 2023, 172 (1-2) : 169 - 207

← 1 2 3 4 5 →