论文标题
关于Chow和Hurwitz形式的复杂性
On the complexity of Chow and Hurwitz forms
论文作者
论文摘要
我们考虑了计算Chow形式的位及其对多主体空间的概括的复杂性。我们使用结果指数开发确定性算法，并获得单个指数复杂性上限。 Chow形式的早期计算结果是算术复杂性模型，我们的结果代表了第一个位复杂性结合。我们还将算法扩展到投影空间中的Hurwitz形式，并探索多主体Hurwitz形式与Matroid理论之间的联系。我们工作的动机来自发病率的几何形状，其中有趣的计算代数问题仍然开放。
We consider the bit complexity of computing Chow forms and their generalization to multiprojective spaces. We develop a deterministic algorithm using resultants and obtain a single exponential complexity upper bound. Earlier computational results for Chow forms were in the arithmetic complexity model, and our result represents the first bit complexity bound. We also extend our algorithm to Hurwitz forms in projective space, and explore connections between multiprojective Hurwitz forms and matroid theory. The motivation for our work comes from incidence geometry where intriguing computational algebra problems remain open.
