代数方程与凸体
Algebraic equations and convex bodies
摘要：
著名的伯恩斯坦-库什尼连科定理来自牛顿多面体理论，涉及代数几何和混合体积理论。最近，作者发现了一个深远的推广这一定理的一般系统的代数方程组的任何拟射影簇。在本说明中，我们回顾这些结果及其应用代数几何和凸几何。
英文摘要：
The well-known Bernstein-Kushnirenko theorem from the theory of Newton polyhedra relates algebraic geometry and the theory of mixed volumes. Recently the authors have found a far-reaching generalization of this theorem to generic systems of algebraic equations on any quasi-projective variety. In the present note we review these results and their applications to algebraic geometry and convex geometry.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
