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Subadditivity of Syzygies of Ideals and Related Problems

In: Commutative Algebra

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  • Jason McCullough

    (Iowa State University, Department of Mathematics)

Abstract

In this paper we survey what is known about the maximal degrees of minimal syzygies of graded ideals over polynomial rings. Subadditivity is one such property that is conjectured to hold for certain classes of rings but fails in general. We discuss bounds on degrees of syzygies and regularity given partial information about the beginning of a free resolution, such as degrees of generators or degrees of first syzygies. We also focus specifically on conditions that guarantee an ideal is quadratic with linear resolution for a fixed number of steps. Finally we collect some old and new open problems on degrees of syzygies.

Suggested Citation

  • Jason McCullough, 2021. "Subadditivity of Syzygies of Ideals and Related Problems," Springer Books, in: Irena Peeva (ed.), Commutative Algebra, pages 501-522, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-89694-2_16
    DOI: 10.1007/978-3-030-89694-2_16
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