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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
4. Main results
4.1. Wall crossing and tilting equivalence. This section shows that wall-crossings of magic windows correspond to equivalences that are induced by tilting modules.
Proof. By Teleman’s quantization theorem [Tel], for all k ∈ Z, the natural restriction map induces an isomorphism
of equivalences is commutative.
Proof. (1) The adjunction gives an isomorphism
Therefore we only need to prove that the right hand sides of (4.E) and (4.F) are isomorphic functors. But this follows from a natural isomorphism
Lemma 4.8. Notation is same as above.
(2) This also follows from Lemma 3.19 and the fact that µδ,δ′ is a bijection.
(3) This is a consequence of (2).
For each F ∈ F(δ,δ′)
Theorem 4.9. Notation is same as above.
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This paper is available on arxiv under CC0 1.0 DEED license.
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