Orlov's functors in Macaulay2

Abstract

Given a commutative and graded Gorenstein ring $R$ with associated projective variety $X$, a theorem of Orlov gives fully faithful embeddings from the graded singularity category of $R$ to the derived category of $X$, or vice versa, depending on the degree of the canonical bundle of $X$. We describe algorithms for computing these embeddings that can be implemented in Macaulay2.

This is a preliminary draft. When the accompanying Macaulay2 package is complete, we will update this article with example computations using our code