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Brasselet number and Newton polygons

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Abstract

We present a formula to compute the Brasselet number of \(f:(Y,0)\rightarrow (\mathbb {C}, 0)\) where \(Y\subset X\) is a non-degenerate complete intersection in a toric variety X. As applications we establish several results concerning invariance of the Brasselet number for families of non-degenerate complete intersections. Moreover, when \((X,0) = (\mathbb {C}^n,0)\) we derive sufficient conditions to obtain the invariance of the Euler obstruction for families of complete intersections with an isolated singularity which are contained in X.

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Acknowledgements

The authors are grateful to Nivaldo de Góes Grulha Jr. from ICMC-USP for helpful conversations in developing this paper and to Bruna Oréfice Okamoto from DM-UFSCar for helpful conversations about the Bruce–Roberts’ Milnor number. Through the project CAPES/PVE Grant 88881. 068165/2014-01 of the program Science without borders, Professor Mauro Spreafico visited the DM-UFSCar in São Carlos providing useful discussions with the authors. Moreover, the authors were partially supported by this project, therefore we are grateful to this program. We would like to thank the referee for many valuable suggestions which improved this paper.

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  1. Department of Mathematics, Universidade Federal de São Carlos (UFSCar), São Carlos, Brazil

    Thaís M. Dalbelo & Luiz Hartmann

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  1. Thaís M. Dalbelo
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Luiz Hartmann is Partially support by FAPESP: 2016/16949-8 and both authors are partially supported by CAPES/PVE:88881.068165/2014-01.

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Dalbelo, T.M., Hartmann, L. Brasselet number and Newton polygons. manuscripta math. 162, 241–269 (2020). https://doi.org/10.1007/s00229-019-01125-w

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