Syzygies and cohomology (A08)

Syzygies在计算代数几何中占有重要地位。它们构成了基本算法和结构的基石。例如，射影变异上相干束上同调的计算是基于外部代数上的协同计算。在这个项目中，我们计划从理论和计算机代数的角度进一步推进协同的概念。目标是一种计算更高直接图像复合体的算法，改进和并行化基本协同算法，研究协同的渐近性。

Syzygies play an important role in computational algebraic geometry. They form a cornerstone for basic algorithms and constructions. For example, the computation of coherent sheaf cohomology on projective varieties is based on syzygy computations over exterior algebras via the theory of Tate resolutions. In this project we plan to advance the concept of syzygies further, both from a theoretical and from a computer algebra point of view. Goals are an algorithm to compute higher direct image complexes, improvement and parallelization of the basic syzygy algorithm and the investigation of asymptotics of syzygies.