10 citations · 25 across the 13 of their papers we have counts for
5 papers · 1 filter
Orlov's functors in Macaulay2
Michael K. Brown, Souvik Dey, Geoffrey Fatin +3
Given a commutative and graded Gorenstein ring with associated projective variety , a theorem of Orlov gives fully faithful embeddings from the graded singularity category o…
Computing Direct Sum Decompositions
Devlin Mallory, Mahrud Sayrafi
We describe and prove correctness of two practical algorithms for finding indecomposable summands of finitely generated modules over a finitely generated k-algebra R. The first alg…
Bounds on Multigraded Regularity
Juliette Bruce, Lauren Cranton Heller, Mahrud Sayrafi
Multigraded Castelnuovo--Mumford regularity of a module over the total coordinate ring of a smooth projective toric variety is a region $\operatorname{reg} M \subset \o…
Characterizing Multigraded Regularity and Virtual Resolutions on Products of Projective Spaces
Juliette Bruce, Lauren Cranton Heller, Mahrud Sayrafi
We explore the relationship between multigraded Castelnuovo--Mumford regularity, truncations, Betti numbers, and virtual resolutions on a product of projective spaces . After pr…
Computations over Local Rings in Macaulay2
Mahrud Sayrafi
Local rings are ubiquitous in algebraic geometry. Not only are they naturally meaningful in a geometric sense, but also they are extremely useful as many problems can be attacked b…