Mutations of noncommutative crepant resolutions: Appendix A. Matrix factorizations

9 Jun 2024


(1) Wahei Hara;

(2) Yuki Hirano.

Appendix A. Matrix factorizations

This appendix recalls definitions and fundamental properties of derived factorization categories. See [Pos, BFK1, BDFIK, Hir1, Hir3] for more details.

where W in the left LG model denotes f ∗W by abuse of notation, and the functor (A.A) defines the right derived functor

The following shows an equivariant and factorization version of a tilting equivalence.

Lemma A.6 ([BFK1, Proposition 3.20][1]). Assume that the sections s and t ∗ are regular. Then there are isomorphisms

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[1] There is a typo in the latter assertion in loc. cit.