# The Multiplicity Polar Theorem, collections of 1-forms and Chern numbers

@article{Gaffney2011TheMP,
title={The Multiplicity Polar Theorem, collections of 1-forms and Chern numbers},
author={Terence Gaffney and Nivaldo G. Grulha},
journal={arXiv: Complex Variables},
year={2011}
}
• Published 30 December 2011
• Mathematics
• arXiv: Complex Variables
In this work we show how the Multiplicity Polar Theorem can be used to calculate Chern numbers for a collection of 1-forms.
8 Citations
The Euler obstruction and the Chern obstruction
• Mathematics
• 2010
In this work we determine relations between the local Euler obstruction of an analytic map f and the Chern obstruction of a convenient collection of 1‐forms associated to f. We give applications to
Indices of vector fields and 1-forms
• Mathematics
• 2021
We discuss the notions of indices of vector fields and 1-forms and their generalizations to singular varieties and varieties with actions of finite groups, as well as indices of collections of vector
Equisingularity and the Theory of Integral Closure
This is an introduction to the study of the equisingularity of sets using the theory of the integral closure of ideals and modules as the main tool. It introduces the notion of the landscape of a
Codimension Two Determinantal Varieties with Isolated Singularities
• Mathematics
• 2011
We study codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their
The theorem of HilbertBurch provides a good description of codimension two determinantal varieties and their deformations in terms of their presentation matrices. In this work we use this
Pairs of modules and determinantal isolated singularities
• Mathematics
• 2014
We continue the development of the study of the equisingularity of isolated singularities, in the determinantal case. This version of the paper includes a substantial amount of new material (76%
The geometrical information encoded by the Euler obstruction of a map
• Mathematics
International Journal of Mathematics
• 2022
In this work, we investigate the topological information captured by the Euler obstruction of a map-germ, [Formula: see text], where [Formula: see text] denotes a germ of a complex [Formula: see
Poincar\'e-Hopf Theorem for Isolated Determinantal Singularities.
• Mathematics
• 2020
Let $X \subset\mathbb{P}^r$ be a projective $d$-variety with isolated determinantal singularities and $\omega$ be a $1$-form on $X$ with a finite number of singularities (in the stratified sense).

## References

SHOWING 1-10 OF 32 REFERENCES
The Euler obstruction and the Chern obstruction
• Mathematics
• 2010
In this work we determine relations between the local Euler obstruction of an analytic map f and the Chern obstruction of a convenient collection of 1‐forms associated to f. We give applications to
Milnor numbers and Euler obstruction*
• Mathematics
• 2003
Abstract.Using a geometric approach, we determine the relations between the local Euler obstruction Euf of a holomorphic function f and several generalizations of the Milnor number for functions on
Indices of Vector Fields and 1-Forms on Singular Varieties
• Mathematics
• 2006
We discuss different generalizations of the classical notion of the index of a singular point of a vector field to the case of vector fields or 1-forms on singular varieties, describe relations
CHERN OBSTRUCTIONS FOR COLLECTIONS OF 1-FORMS ON SINGULAR VARIETIES
• Mathematics
• 2005
W. EBELING AND S. M. GUSEIN-ZADEDedicated to Jean-Paul Brasselet on the occasion of his 60th birthdayAbstract. We introduce a certain index of a collection of germsof 1-forms on a germ of a singular
Commutative Algebra I
1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typed
Commutative Algebra: with a View Toward Algebraic Geometry
Introduction.- Elementary Definitions.- I Basic Constructions.- II Dimension Theory.- III Homological Methods.- Appendices.- Hints and Solutions for Selected Exercises.- References.- Index of
The index of a holomorphic flow with an isolated singularity
• Mathematics
• 1991
The index of a holomorphic vector field Z defined on a germ of a hypersurface V with an isolated singularity is defined. The index coincides with the Hopf index in the smooth case. Formulae for the
Radial Index and Euler Obstruction of a 1-Form on a Singular Variety
• Mathematics
• 2004
A notion of the radial index of an isolated singular point of a 1-form on a singular (real or complex) variety is discussed. For the differential of a function it is related to the Euler
The multiplicity of pairs of modules and hypersurface singularities
This paper applies the multiplicity polar theorem to the study of hypersurfaces with non-isolated singularities. The multiplicity polar theorem controls the multiplicity of a pair of modules in a