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
3. Quasi-symmetric representation and GIT quotient
3.1. Quasi-symmetric representations and magic windows. This section recalls fundamental properties of derived categories of GIT quotients arising from quasi-symmetric representations, which are established in [HSa] and [SV1]. We freely use notation from Section 1.6.
and then it associates the GIT quotient stack [Xss(ℓ)/G].
Proposition 3.10 ([HSa, Proposition 6.2]). There is an equivalence of groupoids
Proposition 3.13 ([HSa, Proposition 6.5]). There is an equivalence
extending the equivalence in Proposition 3.10.
(3) This follows from (2).
The following is elementary, but we give a proof for the convenience of the reader
Proof. If W is trivial, the results are obvious. Thus, assume that W ̸= 1
The following result proves that this map is bijective.
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