论文标题
曲线估值和混合量在理性品种的隐式中
Curve valuations and mixed volumes in the implicitization of rational varieties
论文作者
论文摘要
我们通过曲线估值来解决参数化和规定的支持下的理性品种家庭的热带化描述。考虑到具有非平凡分母的合理参数化，我们通过Sturmfels，Tevelev和YU恢复并扩展结果。我们的观点的优点是可以将其推广以处理非类别的参数化。我们基于组合条件对定义参数化的多项式支持的相对位置进行了详细的封闭图像程度分析。当多项式的支持不同时，我们在该程度上获得了一个新的公式和更细的界限。我们还提出了一个新的公式和在原点处的订单的界限，以防封闭图像是超曲面。
We address the description of the tropicalization of families of rational varieties under parametrizations with prescribed support, via curve valuations. We recover and extend results by Sturmfels, Tevelev and Yu for generic coefficients, considering rational parametrizations with non-trivial denominator. The advantage of our point of view is that it can be generalized to deal with non-generic parametrizations. We provide a detailed analysis of the degree of the closed image, based on combinatorial conditions on the relative positions of the supports of the polynomials defining the parametrization. We obtain a new formula and finer bounds on the degree, when the supports of the polynomials are different. We also present a new formula and bounds for the order at the origin in case the closed image is a hypersurface.
