Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Finding local summands

Seminar | November 26 | 3:45-4:45 p.m. | 939 Evans Hall

 Mengyuan Zhang, UC Berkeley

 Department of Mathematics

The theory of basic elements developed by Eisenbud-Evans is concerned with finding local free summands of a module. A modification of the arguments by Bruns allows one to find local free summands up to a given codimension (or depth). In this expository talk, we discuss this problem in the graded case, where the degrees of the free local summands give extra structure not present in the affine case. This problem is intimately related to the liaison theory of curves in P3, and suggests a liaison theory for sheaves with the same cohomology modules.