Shapes of free resolutions over a local ring

Abstract

We classify the possible shapes of minimal free resolutions over a regular local ring. This illustrates the existence of free resolutions whose Betti numbers behave in surprisingly pathological ways. We also give an asymptotic characterization of the possible shapes of minimal free resolutions over hypersurface rings. Our key new technique uses asymptotic arguments to study formal Q-Betti sequences.

14 pages, 1 figure; v2: sections have been reorganized substantially and exposition has been streamlined

References in corpus (3)

• Tensor complexes: Multilinear free resolutions constructed from higher tensors
• Betti numbers of graded modules and the Multiplicity Conjecture in the non-Cohen-Macaulay case
• Betti Numbers of Syzygies and Cohomology of Coherent Sheaves

Cited by in corpus (7)

• Categorified duality in Boij-Söderberg Theory and invariants of free complexes
• The cone of Betti diagrams over a hypersurface ring of low embedding dimension
• The cone of Betti tables over a rational normal curve
• The cone of Betti tables over three non-collinear points in the plane
• Three flavors of extremal Betti tables
• Questions about Boij-Söderberg theory
• Syzygies of ${\mathbb{P}}^1\times {\mathbb{P}}^1$: data and conjectures