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The Euler obstruction and torus action

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Abstract

In this paper we study surfaces with the property that their irreducible components are toric surfaces. In particular, we present a formula to compute the Euler obstruction of such surfaces. As an application of this formula we compute the Euler obstruction for some families of determinantal surfaces. In the last section, we make some remarks about Milnor number and toric surfaces in \(\mathbb {C}^3\) and \(\mathbb {C}^4\).

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Acknowledgments

The authors are grateful to J.-P. Brasselet and E. M. Bonotto for their careful reading and suggestions. The authors also thank T. Melo for his help with the figure of this work. Through the project Pesquisador Visitante Especial Grant 400580/2012-8 of the program Ciência sem Fronteiras-Brazil professor J.-P. Brasselet visited the ICMC-USP São Carlos, providing useful discussions to the authors, therefore the authors are grateful to this program. The first author was partially supported by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brazil) Grant 8760-11-0 and by CNPQ (Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brazil) Grant 474289/2013-3 and the second author was supported by FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo, Brazil) Grant 2013/11258-9 and by CNPQ Grant 305560/2010-7, 200430/2011-4 and 474289/2013-3.

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Authors and Affiliations

  1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo (USP), São Carlos, Brazil

    T. M. Dalbelo & N. G. Grulha Jr.

  2. Institut de Mathématiques de Luminy, Aix-Marseille Université, Marseille, France

    T. M. Dalbelo

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  1. T. M. Dalbelo
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  2. N. G. Grulha Jr.
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Correspondence to T. M. Dalbelo.

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Dalbelo, T.M., Grulha, N.G. The Euler obstruction and torus action. Geom Dedicata 175, 373–383 (2015). https://doi.org/10.1007/s10711-014-9952-8

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  • DOI: https://doi.org/10.1007/s10711-014-9952-8

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