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摘要翻译：
有理平面曲线隐式方程的牛顿多边形由其任意参数的重数显式确定。基于对Kushnirenko-Bernstein定理的改进，我们给出了这一事实的交集理论证明。我们将这一结果应用于由泛型洛朗多项式或泛型有理函数参数化的曲线的牛顿多边形的确定，并给出了显式泛型条件。我们还证明了给定牛顿多边形的有理曲线的变化是单分的，并计算了它的维数。由此，我们得到了任何具有正面积的凸点阵多边形都是有理平面曲线的牛顿多边形。
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英文标题：
《The Newton polygon of a rational plane curve》
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作者：
Carlos D'Andrea and Martin Sombra
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最新提交年份：
2010
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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英文摘要：
The Newton polygon of the implicit equation of a rational plane curve is explicitly determined by the multiplicities of any of its parametrizations. We give an intersection-theoretical proof of this fact based on a refinement of the Kushnirenko-Bernstein theorem. We apply this result to the determination of the Newton polygon of a curve parameterized by generic Laurent polynomials or by generic rational functions, with explicit genericity conditions. We also show that the variety of rational curves with given Newton polygon is unirational and we compute its dimension. As a consequence, we obtain that any convex lattice polygon with positive area is the Newton polygon of a rational plane curve.
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PDF链接：
https://arxiv.org/pdf/0710.1103
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