Three flavors of extremal Betti tables
Christine Berkesch, Daniel Erman, Manoj Kummini
TL;DR
This paper explores extremal Betti tables across three algebraic contexts, highlighting their unique characteristics and behaviors in polynomial rings, local rings, and bigraded rings.
Contribution
It provides a comparative analysis of extremal Betti tables in different algebraic settings, emphasizing their distinct properties and roles.
Findings
Extremal Betti tables over polynomial rings correspond to pure resolutions.
Behavior of extremal Betti tables differs significantly in local and bigraded rings.
The paper offers insights into the structure and extremality conditions of Betti tables.
Abstract
We discuss extremal Betti tables of resolutions in three different contexts. We begin over the graded polynomial ring, where extremal Betti tables correspond to pure resolutions. We then contrast this behavior with that of extremal Betti tables over regular local rings and over a bigraded ring.
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