Maximal Cohen-Macaulay Complexes and Their Uses: A Partial Survey

Srikanth B. Iyengar (), Linquan Ma (), Karl Schwede () and Mark E. Walker ()
Additional contact information
Srikanth B. Iyengar: University of Utah, Department of Mathematics
Linquan Ma: Purdue University, Department of Mathematics
Karl Schwede: University of Utah, Department of Mathematics
Mark E. Walker: University of Nebraska, Department of Mathematics

A chapter in Commutative Algebra, 2021, pp 475-500 from Springer

Abstract: Abstract This work introduces a notion of complexes of maximal depth, and maximal Cohen-Macaulay complexes, over a commutative noetherian local ring. The existence of such complexes is closely tied to the Hochster’s “homological conjectures”, most of which were recently settled by André. Various constructions of maximal Cohen-Macaulay complexes are described, and their existence is applied to give new proofs of some of the homological conjectures, and also of certain results in birational geometry.

Keywords: Homological conjectures; Maximal Cohen-Macaulay complex; Multiplier ideal; Resolution of singularities; 13D02 (primary); 13D22, 13D45, 14E15, 14F18 (secondary) (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-89694-2_15

Ordering information: This item can be ordered from
http://www.springer.com/9783030896942

DOI: 10.1007/978-3-030-89694-2_15

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().