有理超曲面的线性合偶隐式化：实用综述
Implicitization of rational hypersurfaces via linear syzygies: a practical overview
摘要：
我们在具体条款中揭示了基于合合的算法的一般机制，用于根据多项式中定义参数化的单项式来隐式化有理曲面，遵循并扩展我们与M的联合文章。多姆这些代数技巧是以J.Herzog，A，Simis和W. Vasconcelos是由J. P. Jouanolou湖Busé和M.夏丹他们的工作受到了T. Sederberg和F. Chen，由D.考克斯我们的目标是表达的理论结果和算法到非常具体的条款，避免使用先进的同调交换代数工具，需要他们的证明。
英文摘要：
We unveil in concrete terms the general machinery of the syzygy-based algorithms for the implicitization of rational surfaces in terms of the monomials in the polynomials defining the parametrization, following and expanding our joint article with M. Dohm. These algebraic techniques, based on the theory of approximation complexes due to J. Herzog, A, Simis and W. Vasconcelos, were introduced for the implicitization problem by J.-P. Jouanolou, L. Busé, and M. Chardin. Their work was inspired by the practical method of moving curves, proposed by T. Sederberg and F. Chen, translated into the language of syzygies by D. Cox. Our aim is to express the theoretical results and resulting algorithms into very concrete terms, avoiding the use of the advanced homological commutative algebra tools which are needed for their proofs.
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