Syzygies and cohomology (A08)

合子在计算代数几何中起着重要的作用。它们构成了基本算法和构造的基石。例如，射影簇上的凝聚层上同调的计算是基于Tate归结理论的外部代数上的合运算。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合子的概念。目标是计算高阶直接像复形的算法，对基本合成算法的改进和并行化，以及合成的渐近性的研究。

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.