Homology, Homotopy and Applications
Volume 14 (2012)
Matrix factorizations over projective schemes
Pages: 37 – 61
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.
matrix factorization, singularity category
2010 Mathematics Subject Classification
13D02, 13D09, 14F05