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On Invariants of Generic Slices of Weighted Homogeneous Corank 1 Map Germs from the Plane to 3-Space

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Abstract

In this work, we consider a quasi-homogeneous, corank 1, finitely determined map germ f from \((\mathbb {C}^2,0)\) to \((\mathbb {C}^3,0)\). We consider the invariants m(f(D(f))) and J, where m(f(D(f))) denotes the multiplicity of the image of the double point curve D(f) of f and J denotes the number of tacnodes that appears in a stabilization of the transversal slice curve of \(f(\mathbb {C}^2)\). We present formulas to calculate m(f(D(f))) and J in terms of the weights and degrees of f.

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Acknowledgements

The author warmly thank the referee for very careful reading and valuable comments and suggestions. We would like to thank Jawad Snoussi and Guillermo Peñafort-Sanchis for many helpful conversations, suggestions and comments on this work. The author would like to thank CONACyT for the financial support by Fordecyt 265667 and UNAM/DGAPA for support by PAPIIT IN 113817.

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  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México (UNAM), Cuernavaca, Mexico

    O. N. Silva

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Silva, O.N. On Invariants of Generic Slices of Weighted Homogeneous Corank 1 Map Germs from the Plane to 3-Space. Bull Braz Math Soc, New Series 52, 663–677 (2021). https://doi.org/10.1007/s00574-020-00225-6

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  • DOI: https://doi.org/10.1007/s00574-020-00225-6

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