Thom polynomials for maps of curves with isolated singularities

被引：0

作者：

Kazarian M.E. ^{[1
,2
]}

Lando S.K. ^{[2
,3
]}

机构：

[1] Steklov Institute of Mathematics, Russian Academy of Sciences, Moscow 119991

[2] Laboratoire J.-V. Poncelet, Independent University of Moscow, Moscow 119002

[3] Institute for System Research, Russian Academy of Sciences, Moscow 117218, Nakhimovskii pr. 36

来源：

Proceedings of the Steklov Institute of Mathematics | 2007年 / 258卷 / 1期

基金：

俄罗斯基础研究基金会;

关键词：

STEKLOV Institute; Irreducible Component; Cohomology Class; Basic Classis; Chern Class;

D O I：

10.1134/S0081543807030091

中图分类号：

学科分类号：

摘要：

Thom (residual) polynomials in characteristic classes are used in the analysis of the geometry of function spaces. They serve as a tool for describing the classes that are Poincaré dual to subvarieties of functions with singularities of prescribed types. We give explicit universal expressions for residual polynomials in spaces of functions on complex curves that have isolated singularities and multisingularities, in terms of few characteristic classes. These expressions lead to a partial description of a stratification of Hurwitz spaces. © 2007 Pleiades Publishing, Ltd.

引用

页码：87 / 99

页数：12

共 15 条

[1]

Arnold V.I., Topological Classification of Trigonometric Polynomials and Combinatorics of Graphs with an Equal Number of Vertices and Edges, Funkts. Anal. Prilozh, 30, pp. 1-17, (1996)

[2]

Arnold V.I., Critical Points of Functions and Classification of Caustics, Usp. Mat. Nauk, 29, pp. 243-244, (1974)

[3]

Goulden I.P., Jackson D.M., Vakil R., Towards the Geometry of Double Hurwitz Numbers, Adv. Math., 198, pp. 43-92, (2005)

[4]

Kazaryan M.E., Multisingularities, Cobordisms, and Enumerative Geometry, Usp. Mat. Nauk, 58, pp. 29-88, (2003)

[5]

Kazaryan M.E., Morin Maps and Their Characteristic Classes, (2006)

[6]

Kazaryan M.E., Lando S.K., Towards an Intersection Theory on Hurwitz Spaces, Izv. Ross. Akad. Nauk, Ser. Mat., 68, pp. 91-122, (2004)

[7]

Lando S.K., Zvonkin A.K., Graphs on Surfaces and Their Applications, (2004)

[8]

Zvonkine D., Lando S.K., On Multiplicities of the Lyashko-Looijenga Mapping on Discriminant Strata, Funkts. Anal. Prilozh., 33, pp. 21-34, (1999)

[9]

Lando S., Zvonkine D., Counting Ramified Coverings and Intersection Theory on Spaces of Rational Functions. I: Cohomology of Hurwitz Spaces, Moscow Math. J., 7, pp. 85-107, (2007)

[10]

Looijenga E., The Complement of the Bifurcation Variety of a Simple Singularity, Invent. Math., 23, pp. 105-116, (1974)

← 1 2 →