Boij-Söderberg理论中的偏序集结构
Poset structures in Boij-Söderberg theory
摘要：
Boij-Söderberg理论是对两个锥的研究：射影空间上相干层的上同调表的锥和多项式环上标准分次极小自由分解的锥。每个锥具有由其极值射线上的偏序引起的单纯扇形结构。我们提供了一个新的解释，这些偏序的非零同态的存在，一般和等变的建设。这些结果为Boij-Söderberg理论的核心层和模家族提供了新的见解：超自然层和具有纯分解的Cohen-Macaulay模。此外，我们的结果强烈表明这些偏序的自然性，他们提供的工具，推广Boij-Söderberg理论的其他分次环和投射品种。
英文摘要：
Boij-Söderberg theory is the study of two cones: the cone of cohomology tables of coherent sheaves over projective space and the cone of standard graded minimal free resolutions over a polynomial ring. Each cone has a simplicial fan structure induced by a partial order on its extremal rays. We provide a new interpretation of these partial orders in terms of the existence of nonzero homomorphisms, for both the general and the equivariant constructions. These results provide new insights into the families of sheaves and modules at the heart of Boij-Söderberg theory: supernatural sheaves and Cohen-Macaulay modules with pure resolutions. In addition, our results strongly suggest the naturality of these partial orders, and they provide tools for extending Boij-Söderberg theory to other graded rings and projective varieties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
