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Linear Resolutions of Powers and Products

In: Singularities and Computer Algebra

Author

Listed:
  • Winfried Bruns

    (Universität Osnabrück, Institut für Mathematik)

  • Aldo Conca

    (Università degli Studi di Genova, Dipartimento di Matematica)

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.

Suggested Citation

  • Winfried Bruns & Aldo Conca, 2017. "Linear Resolutions of Powers and Products," Springer Books, in: Wolfram Decker & Gerhard Pfister & Mathias Schulze (ed.), Singularities and Computer Algebra, pages 47-69, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-28829-1_3
    DOI: 10.1007/978-3-319-28829-1_3
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