### Abstract

In this paper, we determine the bifurcation set of a real polynomial function of two variables for non-degenerate case in the sense of Newton polygons by using a toric compactification. We also count the number of singular phenomena at infinity, called “cleaving” and “vanishing”, in the same setting. Finally, we give an upper bound of the number of atypical values at infinity in terms of its Newton polygon. To obtain the upper bound, we apply toric modifications to the singularities at infinity successively.

Original language | English |
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Pages (from-to) | 1201-1222 |

Number of pages | 22 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 71 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2019 Jan 1 |

### Keywords

- Atypical value
- Bifurcation set
- Toric compactification

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Ishikawa, M., Nguyen, T. T., & Pham, T. S. (2019). Bifurcation sets of real polynomial functions of two variables and Newton polygons.

*Journal of the Mathematical Society of Japan*,*71*(4), 1201-1222. https://doi.org/10.2969/jmsj/80518051