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 References [BFK1] M. Ballard, D. Favero and L. Katzarkov, A category of kernels for equivariant factorizations and its implications for Hodge theory. Publ. Math. Inst. Hautes Etudes Sci. ´ 120, 1–111 (2014). 36, 38 [BFK2] M. Ballard, D. Favero and L. Katzarkov, Variation of geometric invariant theory quotients and derived categories, J. Reine Angew. Math. 746, 235–303 (2019). 32, 35 [BDFIK] M. Ballard, D. Deliu, D. Favero, M. U. Isik, and L. Katzarkov, Resolutions in factorization categories. Adv. Math. 295, 195–249 (2016). 34, 36 [BLS] D. Bergh, V. A. Lunts, O. M. Schn¨urer1, Geometricity for derived categories of algebraic stacks, Selecta Math. (N.S.) 22 (2016), no. 4, 2535–2568. 9 [Bri] T. Bridgeland, Flops and derived categories, Invent. Math. 147 (2002), no. 3, 613–632. 1 [BH] W. Bruns and J. Herzog, Cohen-Macaulay rings. Cambridge Studies in Advanced Mathematics, 39. 7, 12 [Che] J.-C. Chen, Flops and equivalences of derived categories for threefolds with only terminal Gorenstein singularities, J. Differential Geom. 61 (2002), no. 2, 227–261. 1 [Har1] W. Hara, Non-commutative crepant resolution of minimal nilpotent orbit closures of type A and Mukai flops. Adv. Math.318(2017), 355–410. 2, 4, 31 [Har2] W. Hara, On derived equivalence for Abuaf flop: mutation of non-commutative crepant resolutions and spherical twists. Matematiche (Catania) 77(2022), no.2, 329–371. 2, 4, 10, 30, 31 [Hal] D. Halpern-Leistner, The derived category of a GIT quotient. J. Amer. Math. Soc. 28 (2015), no. 3, 871–912. 23 [HSa] D. Halpern-Leistner and S. V. Sam, Combinatorial constructions of derived equivalences. J. Amer. Math. Soc. 33, no. 3, 871–912 (2020). 1, 2, 3, 12, 13, 14, 16, 21, 31, 32, 33 [HSh] D. Halpern-Leistner and I. Shipman, Autoequivalences of derived categories via geometric invariant theory. Adv. Math. 303, 1264–1299 (2016). 34, 35 [HN] A. Higashitani and Y. Nakajima, Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions. Selecta Math. (N.S.) 25(2019), no.5, Paper No. 78, 25 pp. 2, 4 [Hir1] Y. Hirano, Equivalences of derived factorization categories of gauged Landau-Ginzburg models. Adv. Math. 306, 200–278 (2017). 36 [Hir2] Y. Hirano, Derived Kn¨orrer periodicity and Orlov’s theorem for gauged Landau-Ginzburg models. Compos. Math. 153, no. 5, 973–1007 (2017). 32 [Hir3] Y. Hirano, Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations . SIGMA Symmetry Integrability Geom. Methods Appl. 17, Paper No. 055, 43 pp (2021). 5, 36, 37, 38 [HW1] Y. Hirano and M. Wemyss, Faithful actions from hyperplane arrangements, Geom. Topol. 22 (2018), no. 6, 3395–3433. 1 [HW2] Y. Hirano and M. Wemyss, Stability conditions for 3-fold flops, arXiv:1907.09742. 1, 3 [HR] J. Hall, D. Rydh, Perfect complexes on algebraic stacks, Compos. Math. 153 (2017), no. 11, 2318–2367. 9 [Isi] M. U. Isik, Equivalence of the derived category of a variety with a singularity category, Int. Math. Res. Not. IMRN (2013), no. 12, 2787–2808. 32 [IR] O. Iyama and I. Reiten, Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras. Am. J. Math. 130 (4), 1087–1149 (2008). 5 [IW1] O. Iyama and M. Wemyss, Maximal modifications and Auslander-Reiten duality for non-isolated singularities. Invent. Math. 197 (2014), no. 3, 521–586. 1, 2, 6, 7, 8, 11 [IW2] O. Iyama and M. Wemyss, Tits cones intersections and applications, preprint. 3 [Kaw] Y. Kawamata, Flops connect minimal models, Publ. RIMS, 44, 419–423 (2008). 1 [KO] N. Koseki and G. Ouchi, Perverse schobers and Orlov equivalences, Eur. J. Math. 9, no. 2, Paper No. 32, 38 pp (2023). 36 [Nak] Y. Nakajima, Mutations of splitting maximal modifying modules: the case of reflexive polygons. Int. Math. Res. Not. IMRN(2019), no.2, 470–550. 2 [OT] C. Okonek and A. Teleman, Graded tilting for gauged Landau-Ginzubrg models and geometric applications. arXiv:1907.10099. 5, 37 [Pos] L. Positselski, Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence. Mem. Amer. Math. Soc. 212 (2011), no. 966. 36 [Shi] I. Shipman, A geometric approach to Orlov’s theorem, Compos. Math. 148, no. 5, 1365-1389 (2012). 32 [SV1] S. ˇ Spenko and M. Van den Bergh, ˇ Non-commutative resolutions of quotient singularities for reductive groups. Invent. Math. 210, no. 1, 3–67 (2017). 1, 12, 21, 22, 25 [SV2] S. ˇ Spenko and M. Van den Bergh, ˇ Non-commutative crepant resolutions for some toric singularities I. Int. Math. Res. Not. IMRN(2020), no.21, 8120–8138. 10 [SV3] S. ˇ Spenko and M. Van den Bergh, ˇ Non-commutative crepant resolutions for some toric singularities. II. J. Noncommut. Geom. 14 (2020), no. 1, 73–103. 9 [SV4] S. ˇ Spenko and M. Van den Bergh, ˇ Tilting bundles on hypertoric varieties. Int. Math. Res. Not. IMRN(2021), no.2, 1034–1042. 31 [SV5] S. ˇ Spenko and M. Van den Bergh, J.-P. Bell, ˇ On the noncommutative Bondal-Orlov conjecture for some toric varieties. Math. Z. 300(2022), no.1, 1055–1068. 2 [Sta] The Stacks Project Authors, Stacks Project. https://stacks.math.columbia.edu 12 [Tel] C. Teleman, The quantization conjecture revisited. Ann. of Math. (2) 152 (2000), no. 1, 1–43. 23, 24 [Van1] M. Van den Bergh, Three-dimensional flops and noncommutative rings, Duke Math. J. 122 (2004), no. 3, 423–455. 1 [Van2] M. Van den Bergh, Non-commutative crepant resolutions. The Legacy of Niels Henrik Abel, pp. 749–770. Springer, Berlin (2004) 1, 2 [Van3] M. Van den Bergh, Non-commutative crepant resolutions, an overview. arXiv:2207.09703. 1, 6, 26 [Wem] M. Wemyss, Flops and Clusters in the Homological Minimal Model Program, Invent. Math. 211 (2018), no. 2, 435–521. 1, 2, 30, 31 Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan Email address: wahei.hara@ipmu.jp Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei, Tokyo 184-8588, Japan Email address: hirano@go.tuat.ac.jp This paper is available on arxiv under CC0 1.0 DEED license. Authors: (1) Wahei Hara; (2) Yuki Hirano. Authors: 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 Abstract and Intro Abstract and Intro Exchanges and Mutations of modifying modules Exchanges and Mutations of modifying modules Quasi-symmetric representation and GIT quotient Quasi-symmetric representation and GIT quotient Main results Main results Applications to Calabi-Yau complete intersections Applications to Calabi-Yau complete intersections Appendix A. Matrix factorizations Appendix A. Matrix factorizations Appendix B. List of Notation Appendix B. List of Notation References References References [BFK1] M. Ballard, D. Favero and L. Katzarkov, A category of kernels for equivariant factorizations and its implications for Hodge theory. Publ. Math. Inst. Hautes Etudes Sci. ´ 120, 1–111 (2014). 36, 38 [BFK2] M. Ballard, D. Favero and L. Katzarkov, Variation of geometric invariant theory quotients and derived categories, J. Reine Angew. Math. 746, 235–303 (2019). 32, 35 [BDFIK] M. Ballard, D. Deliu, D. Favero, M. U. Isik, and L. Katzarkov, Resolutions in factorization categories. Adv. Math. 295, 195–249 (2016). 34, 36 [BLS] D. Bergh, V. A. Lunts, O. M. Schn¨urer1, Geometricity for derived categories of algebraic stacks, Selecta Math. (N.S.) 22 (2016), no. 4, 2535–2568. 9 [Bri] T. Bridgeland, Flops and derived categories, Invent. Math. 147 (2002), no. 3, 613–632. 1 [BH] W. Bruns and J. Herzog, Cohen-Macaulay rings. Cambridge Studies in Advanced Mathematics, 39. 7, 12 [Che] J.-C. Chen, Flops and equivalences of derived categories for threefolds with only terminal Gorenstein singularities, J. Differential Geom. 61 (2002), no. 2, 227–261. 1 [Har1] W. Hara, Non-commutative crepant resolution of minimal nilpotent orbit closures of type A and Mukai flops. Adv. Math.318(2017), 355–410. 2, 4, 31 [Har2] W. Hara, On derived equivalence for Abuaf flop: mutation of non-commutative crepant resolutions and spherical twists. Matematiche (Catania) 77(2022), no.2, 329–371. 2, 4, 10, 30, 31 [Hal] D. Halpern-Leistner, The derived category of a GIT quotient. J. Amer. Math. Soc. 28 (2015), no. 3, 871–912. 23 [HSa] D. Halpern-Leistner and S. V. Sam, Combinatorial constructions of derived equivalences. J. Amer. Math. Soc. 33, no. 3, 871–912 (2020). 1, 2, 3, 12, 13, 14, 16, 21, 31, 32, 33 [HSh] D. Halpern-Leistner and I. Shipman, Autoequivalences of derived categories via geometric invariant theory. Adv. Math. 303, 1264–1299 (2016). 34, 35 [HN] A. Higashitani and Y. Nakajima, Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions. Selecta Math. (N.S.) 25(2019), no.5, Paper No. 78, 25 pp. 2, 4 [Hir1] Y. Hirano, Equivalences of derived factorization categories of gauged Landau-Ginzburg models. Adv. Math. 306, 200–278 (2017). 36 [Hir2] Y. Hirano, Derived Kn¨orrer periodicity and Orlov’s theorem for gauged Landau-Ginzburg models. Compos. Math. 153, no. 5, 973–1007 (2017). 32 [Hir3] Y. Hirano, Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations . SIGMA Symmetry Integrability Geom. Methods Appl. 17, Paper No. 055, 43 pp (2021). 5, 36, 37, 38 [HW1] Y. Hirano and M. Wemyss, Faithful actions from hyperplane arrangements, Geom. Topol. 22 (2018), no. 6, 3395–3433. 1 [HW2] Y. Hirano and M. Wemyss, Stability conditions for 3-fold flops, arXiv:1907.09742. 1, 3 [HR] J. Hall, D. Rydh, Perfect complexes on algebraic stacks, Compos. Math. 153 (2017), no. 11, 2318–2367. 9 [Isi] M. U. Isik, Equivalence of the derived category of a variety with a singularity category, Int. Math. Res. Not. IMRN (2013), no. 12, 2787–2808. 32 [IR] O. Iyama and I. Reiten, Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras. Am. J. Math. 130 (4), 1087–1149 (2008). 5 [IW1] O. Iyama and M. Wemyss, Maximal modifications and Auslander-Reiten duality for non-isolated singularities. Invent. Math. 197 (2014), no. 3, 521–586. 1, 2, 6, 7, 8, 11 [IW2] O. Iyama and M. Wemyss, Tits cones intersections and applications, preprint. 3 [Kaw] Y. Kawamata, Flops connect minimal models, Publ. RIMS, 44, 419–423 (2008). 1 [KO] N. Koseki and G. Ouchi, Perverse schobers and Orlov equivalences, Eur. J. Math. 9, no. 2, Paper No. 32, 38 pp (2023). 36 [Nak] Y. Nakajima, Mutations of splitting maximal modifying modules: the case of reflexive polygons. Int. Math. Res. Not. IMRN(2019), no.2, 470–550. 2 [OT] C. Okonek and A. Teleman, Graded tilting for gauged Landau-Ginzubrg models and geometric applications. arXiv:1907.10099. 5, 37 [Pos] L. Positselski, Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence. Mem. Amer. Math. Soc. 212 (2011), no. 966. 36 [Shi] I. Shipman, A geometric approach to Orlov’s theorem, Compos. Math. 148, no. 5, 1365-1389 (2012). 32 [SV1] S. ˇ Spenko and M. Van den Bergh, ˇ Non-commutative resolutions of quotient singularities for reductive groups. Invent. Math. 210, no. 1, 3–67 (2017). 1, 12, 21, 22, 25 [SV2] S. ˇ Spenko and M. Van den Bergh, ˇ Non-commutative crepant resolutions for some toric singularities I. Int. Math. Res. Not. IMRN(2020), no.21, 8120–8138. 10 [SV3] S. ˇ Spenko and M. Van den Bergh, ˇ Non-commutative crepant resolutions for some toric singularities. II. J. Noncommut. Geom. 14 (2020), no. 1, 73–103. 9 [SV4] S. ˇ Spenko and M. Van den Bergh, ˇ Tilting bundles on hypertoric varieties. Int. Math. Res. Not. IMRN(2021), no.2, 1034–1042. 31 [SV5] S. ˇ Spenko and M. Van den Bergh, J.-P. Bell, ˇ On the noncommutative Bondal-Orlov conjecture for some toric varieties. Math. Z. 300(2022), no.1, 1055–1068. 2 [Sta] The Stacks Project Authors, Stacks Project. https://stacks.math.columbia.edu 12 [Tel] C. Teleman, The quantization conjecture revisited. Ann. of Math. (2) 152 (2000), no. 1, 1–43. 23, 24 [Van1] M. Van den Bergh, Three-dimensional flops and noncommutative rings, Duke Math. J. 122 (2004), no. 3, 423–455. 1 [Van2] M. Van den Bergh, Non-commutative crepant resolutions. The Legacy of Niels Henrik Abel, pp. 749–770. Springer, Berlin (2004) 1, 2 [Van3] M. Van den Bergh, Non-commutative crepant resolutions, an overview. arXiv:2207.09703. 1, 6, 26 [Wem] M. Wemyss, Flops and Clusters in the Homological Minimal Model Program, Invent. Math. 211 (2018), no. 2, 435–521. 1, 2, 30, 31 Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan Email address: wahei.hara@ipmu.jp Email address: wahei.hara@ipmu.jp Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei, Tokyo 184-8588, Japan Email address: hirano@go.tuat.ac.jp Email address: hirano@go.tuat.ac.jp This paper is available on arxiv under CC0 1.0 DEED license. This paper is available on arxiv under CC0 1.0 DEED license. available on arxiv

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Mutations of noncommutative crepant resolutions: Main results

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Acknowledgements, Declarations, Data Availability Statement, and References

Mutations of noncommutative crepant resolutions: Exchanges & Mutations of modifying modules

Mutations of noncommutative crepant resolutions: Quasi-symmetric representation and GIT quotient

Mutations of noncommutative crepant resolutions: Appendix A. Matrix factorizations

Mutations of noncommutative crepant resolutions: Abstract and Intro

Acknowledgements, Declarations, Data Availability Statement, and References

Mutations of noncommutative crepant resolutions: Exchanges & Mutations of modifying modules

Mutations of noncommutative crepant resolutions: Quasi-symmetric representation and GIT quotient

Mutations of noncommutative crepant resolutions: Appendix A. Matrix factorizations

Mutations of noncommutative crepant resolutions: Abstract and Intro

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