Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

   
 

 

Euler obstruction and polar multiplicities of images of finite morphisms on ICIS


Authors: R. Callejas-Bedregal, M. J. Saia and J. N. Tomazella
Journal: Proc. Amer. Math. Soc. 140 (2012), 855-863
MSC (2010): Primary 32S30; Secondary 32S10
Published electronically: June 29, 2011
MathSciNet review: 2869070
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Abstract: We show how to compute the local polar multiplicities of a germ at zero of an analytic variety $ Y$ in $ \mathbb{C}^p$, which is the image by a finite morphism $ f: Z \to Y$, of a $ d$-dimensional isolated complete intersection singularity $ Z$ in $ \mathbb{C}^n$. We also show how to compute the local Euler obstruction of $ Y$ at zero in the case that it is reduced. For this we apply the formula due to Lê and Teissier which describes the local Euler obstruction as an alternating sum of the local polar multiplicities.


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R. Callejas-Bedregal
Affiliation: Departamento de Matemática, UFPB Campus I, Cidade Universitária 58.051-900, João Pessoa, PB, Brazil
Email: roberto@mat.ufpb.br

M. J. Saia
Affiliation: Departamento de Matemática, ICMC-USP, Caixa Postal 668, 13560-970 São Carlos, SP, Brazil
Email: mjsaia@icmc.usp.br

J. N. Tomazella
Affiliation: Departamento de Matemática, UFSCar, Caixa Postal 676, 13565-905 São Carlos, SP, Brazil
Email: tomazella@dm.ufscar.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11125-0
Keywords: Local Euler obstruction, polar multiplicity, complete intersection
Received by editor(s): April 6, 2009
Received by editor(s) in revised form: December 7, 2010
Published electronically: June 29, 2011
Additional Notes: The first-named author is partially supported by CAPES-Procad grant 190-2007; CNPq, grant 620108/2008-8; and FAPESP, grant 2010/03525-9
The second- and third-named authors are partially supported by CNPq, grant 300733/2009-7; CAPES, grant 222/2010; and FAPESP, grant 2008/54222-6
Communicated by: Ted Chinburg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.