Orlov's functors in Macaulay2

Michael K. Brown; Souvik Dey; Geoffrey Fatin; Guanyu Li; Mahrud Sayrafi; Tim Tribone

Orlov's functors in Macaulay2

Commutative Algebra 2026-03-25 v1 Algebraic Geometry

Authors: Michael K. Brown , Souvik Dey , Geoffrey Fatin , Guanyu Li , Mahrud Sayrafi , Tim Tribone

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.

Keywords

functors in category theory

Cite

@article{arxiv.2603.23176,
  title  = {Orlov's functors in Macaulay2},
  author = {Michael K. Brown and Souvik Dey and Geoffrey Fatin and Guanyu Li and Mahrud Sayrafi and Tim Tribone},
  journal= {arXiv preprint arXiv:2603.23176},
  year   = {2026}
}

Comments

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

Orlov's functors in Macaulay2

Abstract

Keywords

Cite

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