Geometry & Topology Volume 26, issue 8 (2022)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Homological mirror symmetry for log Calabi–Yau surfaces

Paul Hacking and Ailsa Keating

Appendix: Wendelin Lutz

Geometry & Topology 26 (2022) 3747–3833

DOI: 10.2140/gt.2022.26.3747

Bibliography

1	M Abouzaid, Homogeneous coordinate rings and mirror symmetry for toric varieties, Geom. Topol. 10 (2006) 1097 MR2240909
2	M Abouzaid, Morse homology, tropical geometry, and homological mirror symmetry for toric varieties, Selecta Math. 15 (2009) 189 MR2529936
3	M Abouzaid, D Auroux, L Katzarkov, Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces, Publ. Math. Inst. Hautes Études Sci. 123 (2016) 199 MR3502098
4	M Abouzaid, P Seidel, Lefschetz fibration techniques in wrapped Floer cohomology, in preparation
5	B Acu, O Capovilla-Searle, A Gadbled, A Marinković, E Murphy, L Starkston, A Wu, An introduction to Weinstein handlebodies for complements of smoothed toric divisors, from: "Research directions in symplectic and contact geometry and topology" (editors B Acu, C Cannizzo, D McDuff, Z Myer, Y Pan, L Traynor), Assoc. Women Math. Ser. 27, Springer (2021) 217 MR4417717
6	D Auroux, Mirror symmetry and T–duality in the complement of an anticanonical divisor, J. Gökova Geom. Topol. 1 (2007) 51 MR2386535
7	D Auroux, Special Lagrangian fibrations, wall-crossing, and mirror symmetry, from: "Surveys in differential geometry, XIII : Geometry, analysis, and algebraic geometry" (editors H D Cao, S T Yau), Surv. Differ. Geom. 13, International (2009) 1 MR2537081
8	D Auroux, L Katzarkov, D Orlov, Mirror symmetry for del Pezzo surfaces : vanishing cycles and coherent sheaves, Invent. Math. 166 (2006) 537 MR2257391
9	D Auroux, L Katzarkov, D Orlov, Mirror symmetry for weighted projective planes and their noncommutative deformations, Ann. of Math. 167 (2008) 867 MR2415388
10	A A Beilinson, Coherent sheaves on Pⁿ and problems in linear algebra, Funktsional. Anal. i Prilozhen. 12 (1978) 68 MR509388
11	P Biran, O Cornea, Lagrangian cobordism, I, J. Amer. Math. Soc. 26 (2013) 295 MR3011416
12	J Blanc, Symplectic birational transformations of the plane, Osaka J. Math. 50 (2013) 573 MR3080816
13	T Bridgeland, D Stern, Helices on del Pezzo surfaces and tilting Calabi–Yau algebras, Adv. Math. 224 (2010) 1672 MR2646308
14	R Casals, E Murphy, Legendrian fronts for affine varieties, Duke Math. J. 168 (2019) 225 MR3909897
15	K Chan, SYZ mirror symmetry for toric varieties, from: "Handbook for mirror symmetry of Calabi–Yau & Fano manifolds" (editors L Ji, B Wu, S T Yau), Adv. Lect. Math. 47, International (2020) 1 MR4237876
16	K Chan, C H Cho, S C Lau, H H Tseng, Gross fibrations, SYZ mirror symmetry, and open Gromov–Witten invariants for toric Calabi–Yau orbifolds, J. Differential Geom. 103 (2016) 207 MR3504949
17	K Chan, S C Lau, N C Leung, SYZ mirror symmetry for toric Calabi–Yau manifolds, J. Differential Geom. 90 (2012) 177 MR2899874
18	C H Cho, Y G Oh, Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds, Asian J. Math. 10 (2006) 773 MR2282365
19	K Cieliebak, Y Eliashberg, From Stein to Weinstein and back : symplectic geometry of affine complex manifolds, 59, Amer. Math. Soc. (2012) MR3012475
20	A Corti, A S Kaloghiros, The Sarkisov program for Mori fibred Calabi–Yau pairs, Algebr. Geom. 3 (2016) 370 MR3504536
21	P Deligne, Théorie de Hodge, II, Inst. Hautes Études Sci. Publ. Math. 40 (1971) 5 MR498551
22	G Dimitroglou Rizell, E Goodman, A Ivrii, Lagrangian isotopy of tori in S² ×S² and ℂP², Geom. Funct. Anal. 26 (2016) 1297 MR3568033
23	P Engel, R Friedman, Smoothings and rational double point adjacencies for cusp singularities, J. Differential Geom. 118 (2021) 23 MR4255071
24	B Fang, C C M Liu, D Treumann, E Zaslow, T-duality and homological mirror symmetry for toric varieties, Adv. Math. 229 (2012) 1875 MR2871160
25	A Fathi, F Laudenbach, V Poénaru, Thurston’s work on surfaces, 48, Princeton Univ. Press (2012) MR3053012
26	R Friedman, On the geometry of anticanonical pairs, (2015) arXiv:1502.02560
27	W Fulton, Introduction to toric varieties, 131, Princeton Univ. Press (1993) MR1234037
28	M Futaki, K Ueda, Exact Lefschetz fibrations associated with dimer models, Math. Res. Lett. 17 (2010) 1029 MR2729627
29	S Ganatra, J Pardon, V Shende, Sectorial descent for wrapped Fukaya categories, (2019) arXiv:1809.03427v2
30	E Giroux, Géométrie de contact : de la dimension trois vers les dimensions supérieures, from: "Proceedings of the International Congress of Mathematicians" (editors S Y Jang, Y R Kim, D W Lee, I Ye), Higher Ed. Press (2002) 405 MR1957051
31	E Giroux, J Pardon, Existence of Lefschetz fibrations on Stein and Weinstein domains, Geom. Topol. 21 (2017) 963 MR3626595
32	A B Givental, Homological geometry and mirror symmetry, from: "Proceedings of the International Congress of Mathematicians" (editor S D Chatterji), Birkhäuser (1995) 472 MR1403947
33	A L Gorodentsev, S A Kuleshov, Helix theory, Mosc. Math. J. 4 (2004) 377 MR2108443
34	M Gross, Special Lagrangian fibrations, I : Topology, from: "Integrable systems and algebraic geometry" (editors M H Saito, Y Shimizu, K Ueno), World Sci. (1998) 156 MR1672120
35	M Gross, Special Lagrangian fibrations, II : Geometry—A survey of techniques in the study of special Lagrangian fibrations, from: "Surveys in differential geometry: differential geometry inspired by string theory" (editor S T Yau), Surv. Differ. Geom. 5, International (1999) 341 MR1772274
36	M Gross, P Hacking, S Keel, Birational geometry of cluster algebras, Algebr. Geom. 2 (2015) 137 MR3350154
37	M Gross, P Hacking, S Keel, Mirror symmetry for log Calabi–Yau surfaces, I, Publ. Math. Inst. Hautes Études Sci. 122 (2015) 65 MR3415066
38	M Gross, P Hacking, S Keel, Moduli of surfaces with an anti-canonical cycle, Compos. Math. 151 (2015) 265 MR3314827
39	M Gross, B Siebert, Mirror symmetry via logarithmic degeneration data, I, J. Differential Geom. 72 (2006) 169 MR2213573
40	M Gross, B Siebert, Mirror symmetry via logarithmic degeneration data, II, J. Algebraic Geom. 19 (2010) 679 MR2669728
41	M Gross, B Siebert, From real affine geometry to complex geometry, Ann. of Math. 174 (2011) 1301 MR2846484
42	A Hanlon, Monodromy of monomially admissible Fukaya–Seidel categories mirror to toric varieties, Adv. Math. 350 (2019) 662 MR3948684
43	K Hori, Mirror symmetry and quantum geometry, from: "Proceedings of the International Congress of Mathematicians" (editors S Y Jang, Y R Kim, D W Lee, I Ye), Higher Ed. Press (2002) 431 MR1957551
44	K Hori, C Vafa, Mirror symmetry, (2000) arXiv:hep-th/0002222
45	D Huybrechts, Fourier–Mukai transforms in algebraic geometry, Clarendon (2006) MR2244106
46	A Keating, Homological mirror symmetry for hypersurface cusp singularities, Selecta Math. 24 (2018) 1411 MR3782425
47	A Keating, On symplectic stabilisations and mapping classes, Bull. Lond. Math. Soc. 54 (2022) 718 MR4453701
48	O van Koert, Lecture notes on stabilization of contact open books, Münster J. Math. 10 (2017) 425 MR3725503
49	J Kollár, K E Smith, A Corti, Rational and nearly rational varieties, 92, Cambridge Univ. Press (2004) MR2062787
50	M. Kontsevich, lecture notes taken by J Bellaiche, J-F Dat, I Marin, G Racinet and H Randriambololona (1998)
51	S A Kuleshov, D O Orlov, Exceptional sheaves on Del Pezzo surfaces, Izv. Ross. Akad. Nauk Ser. Mat. 58 (1994) 53 MR1286839
52	Y Lekili, T Perutz, Arithmetic mirror symmetry for the 2–torus, (2012) arXiv:1211.4632
53	Y Lekili, A Polishchuk, Arithmetic mirror symmetry for genus 1 curves with n marked points, Selecta Math. 23 (2017) 1851 MR3663596
54	E Looijenga, Rational surfaces with an anticanonical cycle, Ann. of Math. 114 (1981) 267 MR632841
55	V A Lunts, D O Orlov, Uniqueness of enhancement for triangulated categories, J. Amer. Math. Soc. 23 (2010) 853 MR2629991
56	J Milnor, Lectures on the h–cobordism theorem, Princeton Univ. Press (1965) MR0190942
57	H Ohta, K Ono, Symplectic fillings of the link of simple elliptic singularities, J. Reine Angew. Math. 565 (2003) 183 MR2024651
58	D O Orlov, Projective bundles, monoidal transformations, and derived categories of coherent sheaves, Izv. Ross. Akad. Nauk Ser. Mat. 56 (1992) 852 MR1208153
59	J Pascaleff, Floer cohomology in the mirror of the projective plane and a binodal cubic curve, Duke Math. J. 163 (2014) 2427 MR3265556
60	M Perling, Combinatorial aspects of exceptional sequences on (rational) surfaces, Math. Z. 288 (2018) 243 MR3774412
61	A Polishchuk, E Zaslow, Categorical mirror symmetry: the elliptic curve, Adv. Theor. Math. Phys. 2 (1998) 443 MR1633036
62	L Polterovich, The surgery of Lagrange submanifolds, Geom. Funct. Anal. 1 (1991) 198 MR1097259
63	P Seidel, More about vanishing cycles and mutation, from: "Symplectic geometry and mirror symmetry" (editors K Fukaya, Y G Oh, K Ono, G Tian), World Sci. (2001) 429 MR1882336
64	P Seidel, A long exact sequence for symplectic Floer cohomology, Topology 42 (2003) 1003 MR1978046
65	P Seidel, A_∞–subalgebras and natural transformations, Homology Homotopy Appl. 10 (2008) 83 MR2426130
66	P Seidel, Fukaya categories and Picard–Lefschetz theory, Eur. Math. Soc. (2008) MR2441780
67	P Seidel, Symplectic homology as Hochschild homology, from: "Algebraic geometry, I" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 415 MR2483942
68	P Seidel, Fukaya A_∞–structures associated to Lefschetz fibrations, I, J. Symplectic Geom. 10 (2012) 325 MR2983434
69	P Seidel, Fukaya A_∞–structures associated to Lefschetz fibrations, II, from: "Algebra, geometry, and physics in the 21st century" (editors D Auroux, L Katzarkov, T Pantev, Y Soibelman, Y Tschinkel), Progr. Math. 324, Springer (2017) 295 MR3727564
70	P Seidel, R Thomas, Braid group actions on derived categories of coherent sheaves, Duke Math. J. 108 (2001) 37 MR1831820
71	V Shende, D Treumann, H Williams, On the combinatorics of exact Lagrangian surfaces, (2016) arXiv:1603.07449
72	Z Sylvan, On partially wrapped Fukaya categories, J. Topol. 12 (2019) 372 MR3911570
73	M Symington, Four dimensions from two in symplectic topology, from: "Topology and geometry of manifolds" (editors G Matić, C McCrory), Proc. Sympos. Pure Math. 71, Amer. Math. Soc. (2003) 153 MR2024634
74	K Ueda, Homological mirror symmetry for toric del Pezzo surfaces, Comm. Math. Phys. 264 (2006) 71 MR2212216
75	R Vianna, Infinitely many exotic monotone Lagrangian tori in ℂℙ², J. Topol. 9 (2016) 535 MR3509972
76	R Vianna, Infinitely many monotone Lagrangian tori in del Pezzo surfaces, Selecta Math. 23 (2017) 1955 MR3663599
77	C Voisin, Hodge theory and complex algebraic geometry, I, 76, Cambridge Univ. Press (2002) MR1967689
78	A Weinstein, Contact surgery and symplectic handlebodies, Hokkaido Math. J. 20 (1991) 241 MR1114405