English

Linear resolutions of powers and products

Commutative Algebra 2016-02-26 v1

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 Gr\"obner bases and Sagbi deformation.

Keywords

Cite

@article{arxiv.1602.07996,
  title  = {Linear resolutions of powers and products},
  author = {Winfried Bruns and Aldo Conca},
  journal= {arXiv preprint arXiv:1602.07996},
  year   = {2016}
}