Integration of Buchanan's Method with Koszul-Plücker Theory

In this paper, we integrate Buchanan’s method of orientation-preservingfibers and filters with the Koszul-Pl¨ucker theory. By exploring the rela-tionships between orientation-preserving maps, filters, and zero-fold cov-erings, we derive novel mathematical forms and results. We extend theconcepts of Koszul complexes and Pl¨ucker embeddings, providing detailedproofs and mathematical formulations. Commutative diagrams are usedto illustrate key concepts, and all mathematical statements are presentedwith precision and clarity.