10 citations · 25 across the 13 of their papers we have counts for
13 papers
Weighted Syzygies of Pointed Curves
Maya Banks, John Cobb, Mahrud Sayrafi
For a point on a smooth projective curve of genus , the section ring can be minimally presented as a quotient where is a $…
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…
Seshadri Regions and the Asymptotic Shape of Multigraded Regularity
Juliette Bruce, Lauren Cranton Heller, Mahrud Sayrafi +1
We introduce the Seshadri region of a subvariety, a convex region packaging the classical Seshadri constants with respect to every line bundle simultaneously. We develop the theory…
Computing global Ext for complexes
Michael K. Brown, Souvik Dey, Guanyu Li +1
We give a computational algorithm for computing Ext groups between bounded complexes of coherent sheaves on a projective variety, and we describe an implementation of this algorith…
Connection Matrices in Macaulay2
Paul Görlach, Joris Koefler, Anna-Laura Sattelberger +4
In this article, we describe the theoretical foundations of the Macaulay2 package ConnectionMatrices and explain how to use it. For a left ideal in the Weyl algebra that is of fini…
Splitting of Vector Bundles on Toric Varieties
Mahrud Sayrafi
We prove a Horrocks-type splitting criterion for arbitrary smooth projective toric varieties under an additional hypothesis similar to the case of products of projective spaces by…
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…
A short resolution of the diagonal for smooth projective toric varieties of Picard rank 2
Michael K. Brown, Mahrud Sayrafi
Given a smooth projective toric variety of Picard rank 2, we resolve the diagonal sheaf on by a linear complex of length consisting of finite direct sums…
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…
The Virtual Resolutions Package for Macaulay2
Ayah Almousa, Juliette Bruce, Michael C. Loper +1
We introduce the VirtualResolution package for the computer algebra system Macaulay2. This package has tools to construct, display, and study virtual resolutions for products of 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…
What is the optimal way to prepare a Bell state using measurement and feedback?
Leigh S. Martin, Mahrud Sayrafi, K. Birgitta Whaley
Recent work has shown that use of quantum feedback can significantly enhance both the speed and success rate of measurement-based remote entanglement generation, but it is generall…