Irreducibility of toric complete intersections

Andrey Zhizhin
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Abstract

We develop an approach to study the irreducibility of generic complete intersections in the algebraic torus defined by equations with fixed monomials and fixed linear relations on coefficients. Using our approach we generalize the irreducibility theorems of Khovanskii to fields of arbitrary characteristic. Also we get a combinatorial sufficient conditions for irreducibility of engineered complete intersections. As an application we give a combinatorial condition of irreducibility for some critical loci and Thom-Bordmann strata: $f = f'_x = 0$, $f'_x = f'_y = 0$, $f = f'_x = f'_{xx} = 0$, etc.
环形完全相交的不可还原性
我们开发了一种方法来研究代数环中由具有固定单项式和固定系数线性关系的方程定义的一般完全交点的不可还原性。利用我们的方法,我们将霍万斯基的不可还原性定理推广到任意性质的域。此外,我们还得到了工程完全交集不可还原性的组合充分条件。作为应用,我们给出了一些临界位置和托姆-博德曼阶层的不可还原性组合条件:$f = f'_x = 0$,$f'_x = f'_y = 0$,$f = f'_x = f'_{xx} =0$,等等。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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