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.

翻译：我们研究了计算Chow形式及其在多射影空间推广的比特复杂度。通过运用结式理论，我们构建了一个确定性算法，并获得了单指数复杂度上界。此前关于Chow形式的计算研究停留在算术复杂度模型层面，而本成果首次给出了其比特复杂度界。我们还将该算法推广至射影空间中的Hurwitz形式，并探讨了多射影Hurwitz形式与拟阵理论之间的关联。本研究的动机源于关联几何中若干尚未解决的代数计算难题。