Work

Boij-Söderberg conjectures for differential modules

Year: 2024

Type: article

Abstract: Boij-Söderberg theory gives a combinatorial description of the set of Betti tables belonging to finite length modules over the polynomial ring S=k[x1,…,xn]. We posit that a similar combinatorial description can be given for analogous numerical invariants of graded differential S-modules, which are natural generalizations of chain complexes. We prove several results that lend evidence in support of this conjecture, including a categorical pairing between the derived categories of graded differential S-modules and coherent sheaves on Pn−1 and a proof of the conjecture in the case where S=k[t].

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2024.08.025

Author: Maya Banks

Institution: University of Illinois Chicago

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,140

Funder: University of Wisconsin-Madison