Mutations of noncommutative crepant resolutions: Appendix A. Matrix factorizations

:::info
Authors:

(1) Wahei Hara;

(2) Yuki Hirano.

:::

Table of Links

Abstract and Intro
Exchanges and Mutations of modifying modules
Quasi-symmetric representation and GIT quotient
Main results
Applications to Calabi-Yau complete intersections
Appendix A. Matrix factorizations
Appendix B. List of Notation
References

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

:::info
This paper is available on arxiv under CC0 1.0 DEED license.

:::

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

Leave a Comment

This site uses Akismet to reduce spam. Learn how your comment data is processed.