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Linear Resolutions of Powers and Products

  • Winfried BrunsEmail author
  • Aldo Conca
Chapter
  • 578 Downloads

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 

AMS Subject classes (2010)

13A30 13D02 13C40 13F20 14M12 13P10 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut für MathematikUniversität OsnabrückOsnabrückGermany
  2. 2.Dipartimento di MatematicaUniversità degli Studi di GenovaGenovaItaly

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