Lim Ulrich sequences and Boij-S\"{o}derberg cones
Srikanth B. Iyengar, Linquan Ma, and Mark E. Walker
TL;DR
This paper generalizes the structure of Betti cones from polynomial rings to a broader class of graded rings using lim Ulrich sequences, advancing the understanding of algebraic invariants.
Contribution
It introduces the use of lim Ulrich sequences to extend Boij-Söderberg theory to all finitely generated graded rings with linear Noether normalizations.
Findings
Betti cones characterized for broader class of rings
Existence of lim Ulrich sequences over these rings
Extension of Boij-Söderberg results
Abstract
This paper extends the results of Boij, Eisenbud, Erman, Schreyer, and S\"oderberg on the structure of Betti cones of finitely generated graded modules and finite free complexes over polynomial rings, to all finitely generated graded rings admitting linear Noether normalizations. The key new input is the existence of lim Ulrich sequences of graded modules over such rings.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Rings, Modules, and Algebras