2021/10/20 by Juliette Bruce, Lauren Cranton Heller, Bruce, Juliette +3
Mathematics · #13D02 #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2110.10705
openalex publication_date 2021/10/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We explore the relationship between multigraded Castelnuovo--Mumford regularity, truncations, Betti numbers, and virtual resolutions on a product of projective spaces X. After proving a uniqueness theorem for certain virtual resolutions, we show that the multigraded regularity region of a module M is determined by the minimal graded free resolutions of the truncations M≥\mathbf d for \mathbf d\inPic X. Further, by relating the minimal graded free resolutions of M and M≥\mathbf d we provide a new bound on multigraded regularity of M in terms of its Betti numbers. Using this characterization of regularity and this bound we also compute the multigraded Castelnuovo--Mumford regularity for a wide class of complete intersections in products of projective spaces.