Linear Resolutions of Powers and Products

Winfried Bruns () and Aldo Conca ()
Additional contact information
Winfried Bruns: Universität Osnabrück, Institut für Mathematik
Aldo Conca: Università degli Studi di Genova, Dipartimento di Matematica

A chapter in Singularities and Computer Algebra, 2017, pp 47-69 from Springer

Abstract: Abstract The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms, and Borel-fixed ideals of maximal minors. The main tools are Gröbner bases and Sagbi deformation.

Keywords: Determinantal ideal; Gröbner basis; Ideal of linear forms; Koszul algebra; Linear resolution; Polymatroidal ideal; Primary decomposition; Rees algebra; Regularity; Toric deformation; 13A30; 13D02; 13C40; 13F20; 14M12; 13P10 (search for similar items in EconPapers)
Date: 2017
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:978-3-319-28829-1_3

Ordering information: This item can be ordered from
http://www.springer.com/9783319288291

DOI: 10.1007/978-3-319-28829-1_3

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 ().