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Syzygies of : data and conjectures
Juliette Bruce, Daniel Corey, Daniel Erman +3
We provide a number of new conjectures and questions concerning the syzygies of . The conjectures are based on computing the graded Betti tables an…
Characteristic dependence of syzygies of random monomial ideals
Caitlyn Booms, Daniel Erman, Jay Yang
When do syzygies depend on the characteristic of the field? Even for well-studied families of examples, very little is known. For a family of random monomial ideals, namely the Sta…
Interpolation over ZZ and torsion in class groups
John Berman, Daniel Erman
We prove an interpolation result for homogeneous polynomials over the integers, or more generally for PIDs with finite residue fields. Previous proofs of this result use the well-k…
Cubics in 10 variables vs. cubics in 1000 variables: Uniformity phenomena for bounded degree polynomials
Daniel Erman, Steven V Sam, Andrew Snowden
Hilbert famously showed that polynomials in n variables are not too complicated, in various senses. For example, the Hilbert Syzygy Theorem shows that the process of resolving a mo…