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5 papers
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…
Tate Resolutions on Products of Projective Spaces: Cohomology and Direct Image Complexes
Daniel Erman, David Eisenbud, Frank-Olaf Schreyer
We describe the Macaulay2 package TateOnProducts and its capabilities, which include computing cohomology tables and Beilinson monads of sheaves on products of projective spaces an…
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…
Strength and Hartshorne's Conjecture in high degree
Daniel Erman, Steven V Sam, Andrew Snowden
Hartshorne conjectured that a smooth, codimension c subvariety of n-dimensional projective space must be a complete intersection, whenever c is less than n/3. We prove this in the…