Homology, Homotopy and Applications

Matrix factorizations over projective schemes

Jesse Burke and Mark E. Walker

Full-text: Open access


We study matrix factorizations of regular global sections of line bundles on schemes. If the line bundle is very ample relative to a Noetherian affine scheme we show that morphisms in the homotopy category of matrix factorizations may be computed as the hypercohomology of a certain mapping complex. Using this explicit description, we prove an analogue of Orlov’s theorem that there is a fully faithful embedding of the homotopy category of matrix factorizations into the singularity category of the corresponding zero subscheme. Moreover, we give a complete description of the image of this functor.

Article information

Homology Homotopy Appl., Volume 14, Number 2 (2012), 37-61.

First available in Project Euclid: 12 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 13D09: Derived categories 13D02: Syzygies, resolutions, complexes

Matrix factorization singularity category


Burke, Jesse; Walker, Mark E. Matrix factorizations over projective schemes. Homology Homotopy Appl. 14 (2012), no. 2, 37--61. https://projecteuclid.org/euclid.hha/1355321479

Export citation