Boij-söderberg and Veronese Decompositions
نویسندگان
چکیده
Boij-Söderberg theory has had a dramatic impact on commutative algebra. We determine explicit Boij-Söderberg 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-Söderberg decomposition of an arbitrary homogeneous ideal with a pure resolution changes when multiplying the ideal by a homogeneous polynomial.
منابع مشابه
Boij–Söderberg theory and tensor complexes
The conjectures of M. Boij and J. Söderberg [3], proven by D. Eisenbud and F.-O. Schreyer [8] (see also [7, 4]), link the extremal properties of invariants of graded free resolutions of finitely generated modules over the polynomial ring S = k[x1, . . . , xn] with the Herzog–Huneke–Srinivasan Multiplicity Conjectures. Here k is any field and S has the standard Z-grading. In the course of their ...
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