92 citations · 473 across the 45 of their papers we have counts for
3 papers · 2 filters
The cone of Betti diagrams over a hypersurface ring of low embedding dimension
Christine Berkesch, Jesse Burke, Daniel Erman +1
We give a complete description of the cone of Betti diagrams over a standard graded hypersurface ring of the form k[x,y]/<q>, where q is a homogeneous quadric. We also provide a fi…
Shapes of free resolutions over a local ring
Christine Berkesch, Daniel Erman, Manoj Kummini +1
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…
Tensor complexes: Multilinear free resolutions constructed from higher tensors
Christine Berkesch Zamaere, Daniel Erman, Manoj Kummini +1
The most fundamental complexes of free modules over a commutative ring are the Koszul complex, which is constructed from a vector (i.e., a 1-tensor), and the Eagon-Northcott and th…