Open Access
2017 Boij-Söderberg and Veronese decompositions
Christopher A. Francisco, Jeffrey Mermin, Jay Schweig
J. Commut. Algebra 9(3): 367-386 (2017). DOI: 10.1216/JCA-2017-9-3-367


Boij-S\"oderberg theory has had a dramatic impact on commutative algebra. We determine explicit Boij-S\"oderberg coefficients for ideals with linear resolutions and illustrate how these arise from the usual Eliahou-Kervaire computations for Borel ideals. In addition, we explore a new numerical decomposition for resolutions based on a row-by-row approach; here, the coefficients of the Betti diagrams are not necessarily positive. Finally, we demonstrate how the Boij-S\"oderberg decomposition of an arbitrary homogeneous ideal with a pure resolution changes when multiplying the ideal by a homogeneous polynomial.


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Christopher A. Francisco. Jeffrey Mermin. Jay Schweig. "Boij-Söderberg and Veronese decompositions." J. Commut. Algebra 9 (3) 367 - 386, 2017.


Published: 2017
First available in Project Euclid: 1 August 2017

zbMATH: 06790175
MathSciNet: MR3685048
Digital Object Identifier: 10.1216/JCA-2017-9-3-367

Primary: 13C14 , 13D02

Keywords: Boij-Söderberg theory , Borel ideals , Cohen-Macaulay ideals , pure resolutions , Veronese ideals

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

Vol.9 • No. 3 • 2017
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