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- Title
Categorified duality in Boij-Söderberg theory and invariants of free complexes.
- Authors
Eisenbud, David; Erman, Daniel
- Abstract
We present a robust categorical foundation for the duality theory introduced by Eisenbud and Schreyer to prove the Boij-Söderberg conjectures describing numerical invariants of syzygies. The new foundation allows us to extend the reach of the theory substantially. More explicitly, we construct a pairing between derived categories that simultaneously categorifies all the functionals used by Eisenbud and Schreyer. With this new tool, we describe the cone of Betti tables of finite, minimal free complexes having homology modules of specified dimensions over a polynomial ring, and we treat many examples beyond polynomial rings. We also construct an analogue of our pairing between derived categories on a toric variety, yielding toric/multigraded analogues of the Eisenbud-Schreyer functionals.
- Subjects
INVARIANTS (Mathematics); SYZYGIES (Mathematics); HOMOLOGY theory; MODULES (Algebra); SHEAF cohomology
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2017, Vol 19, Issue 9, p2657
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/725