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Authors:
(1) Wahei Hara;
(2) Yuki Hirano.
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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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This paper is available on arxiv under CC0 1.0 DEED license.
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