The bifurcation set of a complex polynomial function of two variables and the Newton polygons of singularities at infinity

masaharu Ishikawa

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The bifurcation set of a complex polynomial function of two variables and the Newton polygons of singularities at infinity

机译：两个变量的复多项式函数的分叉集和无穷大的奇异性Newton多边形

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A. Nemethi and A. Zaharia have defined the explicit set for a complex polynomial funciton f:C~n→C and conjectured that the bifurcation set of the global fibration of f is given by the union of the set of critical values and the explicit set of f. They have proved only the case n=2 and f is Newton non-degenerate. In the present Paper we will prove this for the case n=2, containing the Newton degenerate case, by Using toric modifications and give an expression of the bifurcation set of f in the words Of Newton polygons.

机译：A. Nemethi和A. Zaharia为复多项式函数f：C〜n→C定义了显式集，并推测f的整体纤维化的分支集由临界值集和显式的并集给出出发。他们证明只有n = 2且f是牛顿非简并的情况。在本文中，我们将通过复曲面修改来证明n = 2的情况（包含牛顿简并的情况），并用牛顿多边形的单词给出f的分叉集的表示。

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来源
《Journal of the Mathematical Society of Japan》 |2002年第1期|p.161-196|共36页
作者
masaharu Ishikawa;
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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类数学;
关键词
complex polynomial functions; bifurcation set; singularities at infinity; Newton polygons;

机译：复杂的多项式函数分叉集无穷大的奇点;牛顿多边形;

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1. Bifurcation sets of real polynomial functions of two variables and Newton polygons [J] . Masaharu Ishikawa, Tat-Thang Nguyen, Tien-San Pham Journal of the Mathematical Society of Japan . 2019,第4期

机译：两个变量和牛顿多边形的实多项式函数的分歧集
2. ON THE BIFURCATION SET OF COMPLEX POLYNOMIAL WITH ISOLATED SINGULARITIES AT INFINITY [J] . Parusinski A. Compositio mathematica . 1995,第3期

机译：无限时具有孤立奇异性的复多项式的分叉集
3. On the bifurcation set of a polynomial function and Newton boundary, II [J] . Alexandru Zaharia Kodai Mathematical Journal . 1996,第2期

机译：关于多项式函数和牛顿边界的分叉集，II
4. LECTURES ON THE TOPOLOGY OF POLYNOMIAL FUNCTIONS AND SINGULARITIES AT INFINITY [C] . DIRK SIERSMA, MIHAI TIBAR School and Workshop on Singularities in Geometry and Topology . 2007

机译：无限远的多项式函数和奇点拓扑讲座
5. Newton polygons of L-functions of polynomials of the form X(d) + Lambda*X. [D] . Yang, Roger Da-Yu. 2001

机译：X（d）+ Lambda * X形式的多项式L函数的牛顿多边形。
6. Light transport in homogeneous tissue with m-dependent anisotropic scattering I: Case’s singular eigenfunctions solution and Chandrasekhar polynomials [O] . Lin Wang, Meng Rong, Kaiyang Li 2018

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7. On the bifurcation set of complex polynomial with isolated singularities at infinity [O] . Parusiński Adam 1995

机译：在无穷大处具有孤立奇点的复多项式的分支集

The bifurcation set of a complex polynomial function of two variables and the Newton polygons of singularities at infinity

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