Geometry & Topology Volume 24, issue 3 (2020)

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The quantum tropical vertex

Pierrick Bousseau

Geometry & Topology 24 (2020) 1297–1379

DOI: 10.2140/gt.2020.24.1297

Bibliography

1	D Abramovich, Q Chen, Stable logarithmic maps to Deligne–Faltings pairs, II, Asian J. Math. 18 (2014) 465 MR3257836
2	D Abramovich, Q Chen, M Gross, B Siebert, Decomposition of degenerate Gromov–Witten invariants, preprint (2017) arXiv:1709.09864
3	D Abramovich, Q Chen, M Gross, B Siebert, Punctured logarithmic curves, preprint (2019)
4	D Abramovich, T Graber, A Vistoli, Gromov–Witten theory of Deligne–Mumford stacks, Amer. J. Math. 130 (2008) 1337 MR2450211
5	D Abramovich, S Marcus, J Wise, Comparison theorems for Gromov–Witten invariants of smooth pairs and of degenerations, Ann. Inst. Fourier (Grenoble) 64 (2014) 1611 MR3329675
6	D Abramovich, J Wise, Birational invariance in logarithmic Gromov–Witten theory, Compos. Math. 154 (2018) 595 MR3778185
7	A Beauville, Sur la cohomologie de certains espaces de modules de fibrés vectoriels, from: "Geometry and analysis" (editor S Ramanan), Tata Inst. Fund. Res., Bombay (1995) 37 MR1351502
8	F Block, L Göttsche, Refined curve counting with tropical geometry, Compos. Math. 152 (2016) 115 MR3453390
9	P Boalch, Hyperkähler manifolds and nonabelian Hodge theory of (irregular) curves, preprint (2012) arXiv:1203.6607
10	P Bousseau, Tropical refined curve counting from higher genera and lambda classes, Invent. Math. 215 (2019) 1 MR3904449
11	P Bousseau, Quantum mirrors of log Calabi–Yau surfaces and higher-genus curve counting, Compos. Math. 156 (2020) 360 MR4048291
12	J Bryan, T Graber, R Pandharipande, The orbifold quantum cohomology of ℂ²∕ℤ₃ and Hurwitz–Hodge integrals, J. Algebraic Geom. 17 (2008) 1 MR2357679
13	J Bryan, R Pandharipande, Curves in Calabi–Yau threefolds and topological quantum field theory, Duke Math. J. 126 (2005) 369 MR2115262
14	S Cecotti, A Neitzke, C Vafa, R–twisting and 4d/2d correspondences, preprint (2010) arXiv:1006.3435
15	S Cecotti, C Vafa, BPS wall crossing and topological strings, preprint (2009) arXiv:0910.2615
16	Q Chen, Stable logarithmic maps to Deligne–Faltings pairs, I, Ann. of Math. 180 (2014) 455 MR3224717
17	W Chen, Y Ruan, Orbifold Gromov–Witten theory, from: "Orbifolds in mathematics and physics" (editors A Adem, J Morava, Y Ruan), Contemp. Math. 310, Amer. Math. Soc. (2002) 25 MR1950941
18	G Ellingsrud, S A Strømme, Towards the Chow ring of the Hilbert scheme of ℙ², J. Reine Angew. Math. 441 (1993) 33 MR1228610
19	C Faber, R Pandharipande, Hodge integrals and Gromov–Witten theory, Invent. Math. 139 (2000) 173 MR1728879
20	L D Faddeev, R M Kashaev, Quantum dilogarithm, Modern Phys. Lett. A 9 (1994) 427 MR1264393
21	S A Filippini, J Stoppa, Block–Göttsche invariants from wall-crossing, Compos. Math. 151 (2015) 1543 MR3383167
22	K Fukaya, Multivalued Morse theory, asymptotic analysis and mirror symmetry, from: "Graphs and patterns in mathematics and theoretical physics" (editors M Lyubich, L Takhtajan), Proc. Sympos. Pure Math. 73, Amer. Math. Soc. (2005) 205 MR2131017
23	W Fulton, Intersection theory, 2, Springer (1998) MR1644323
24	M van Garrel, T Graber, H Ruddat, Local Gromov–Witten invariants are log invariants, Adv. Math. 350 (2019) 860 MR3948687
25	R Gopakumar, C Vafa, M–theory and topological strings, I, preprint (1998) arXiv:hep-th/9809187
26	R Gopakumar, C Vafa, M–theory and topological strings, II, preprint (1998) arXiv:hep-th/9812127
27	T Graber, R Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999) 487 MR1666787
28	M Gross, P Hacking, S Keel, Mirror symmetry for log Calabi–Yau surfaces, I, Publ. Math. Inst. Hautes Études Sci. 122 (2015) 65 MR3415066
29	M Gross, P Hacking, S Keel, M Kontsevich, Canonical bases for cluster algebras, J. Amer. Math. Soc. 31 (2018) 497 MR3758151
30	M Gross, R Pandharipande, Quivers, curves, and the tropical vertex, Port. Math. 67 (2010) 211 MR2662867
31	M Gross, R Pandharipande, B Siebert, The tropical vertex, Duke Math. J. 153 (2010) 297 MR2667135
32	M Gross, B Siebert, From real affine geometry to complex geometry, Ann. of Math. 174 (2011) 1301 MR2846484
33	M Gross, B Siebert, Logarithmic Gromov–Witten invariants, J. Amer. Math. Soc. 26 (2013) 451 MR3011419
34	V Iacovino, Kontsevich–Soibelman wall crossing formula and holomorphic disks, preprint (2017) arXiv:1711.05306
35	I Itenberg, G Mikhalkin, On Block–Göttsche multiplicities for planar tropical curves, Int. Math. Res. Not. 2013 (2013) 5289 MR3142257
36	P Johnson, R Pandharipande, H H Tseng, Abelian Hurwitz–Hodge integrals, Michigan Math. J. 60 (2011) 171 MR2785870
37	D Joyce, Y Song, A theory of generalized Donaldson–Thomas invariants, 1020, Amer. Math. Soc. (2012) MR2951762
38	K Kato, Logarithmic structures of Fontaine–Illusie, from: "Algebraic analysis, geometry, and number theory" (editor J I Igusa), Johns Hopkins Univ. Press, Baltimore, MD (1989) 191 MR1463703
39	S Katz, Genus zero Gopakumar–Vafa invariants of contractible curves, J. Differential Geom. 79 (2008) 185 MR2420017
40	B Kim, H Lho, H Ruddat, The degeneration formula for stable log maps, preprint (2018) arXiv:1803.04210
41	Y Konishi, Integrality of Gopakumar–Vafa invariants of toric Calabi–Yau threefolds, Publ. Res. Inst. Math. Sci. 42 (2006) 605 MR2250076
42	M Kontsevich, Y Soibelman, Affine structures and non–Archimedean analytic spaces, from: "The unity of mathematics" (editors P Etingof, V Retakh, I M Singer), Progr. Math. 244, Birkhäuser, Boston (2006) 321 MR2181810
43	M Kontsevich, Y Soibelman, Stability structures, motivic Donaldson–Thomas invariants and cluster transformations, preprint (2008) arXiv:0811.2435
44	M Kontsevich, Y Soibelman, Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson–Thomas invariants, Commun. Number Theory Phys. 5 (2011) 231 MR2851153
45	M Kontsevich, Y Soibelman, Wall-crossing structures in Donaldson–Thomas invariants, integrable systems and mirror symmetry, from: "Homological mirror symmetry and tropical geometry" (editors R Castano-Bernard, F Catanese, M Kontsevich, T Pantev, Y Soibelman, I Zharkov), Lect. Notes Unione Mat. Ital. 15, Springer (2014) 197 MR3330788
46	P Kucharski, M Reineke, M Stošić, P Sułkowski, BPS states, knots, and quivers, Phys. Rev. D 96 (2017) MR3869892
47	P Kucharski, M Reineke, M Stošić, P Sułkowski, Knots-quivers correspondence, preprint (2017) arXiv:1707.04017
48	J Li, Y Song, Open string instantons and relative stable morphisms, from: "The interaction of finite-type and Gromov–Witten invariants" (editors D Auckly, J Bryan), Geom. Topol. Monogr. 8, Geom. Topol. Publ., Coventry (2006) 49 MR2402819
49	Y S Lin, Correspondence theorem between holomorphic discs and tropical discs on K3 surfaces, preprint (2017) arXiv:1703.00411
50	T Mandel, Scattering diagrams, theta functions, and refined tropical curve counts, preprint (2015) arXiv:1503.06183
51	J Manschot, B Pioline, A Sen, On the Coulomb and Higgs branch formulae for multi-centered black holes and quiver invariants, J. High Energy Phys. (2013) MR3080495
52	E Markman, Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces, Adv. Math. 208 (2007) 622 MR2304330
53	D Maulik, N Nekrasov, A Okounkov, R Pandharipande, Gromov–Witten theory and Donaldson–Thomas theory, I, Compos. Math. 142 (2006) 1263 MR2264664
54	D Maulik, N Nekrasov, A Okounkov, R Pandharipande, Gromov–Witten theory and Donaldson–Thomas theory, II, Compos. Math. 142 (2006) 1286 MR2264665
55	D Maulik, R Pandharipande, R P Thomas, Curves on K3 surfaces and modular forms, J. Topol. 3 (2010) 937 MR2746343
56	S Meinhardt, M Reineke, Donaldson–Thomas invariants versus intersection cohomology of quiver moduli, J. Reine Angew. Math. 754 (2019) 143 MR4000572
57	G Mikhalkin, Enumerative tropical algebraic geometry in ℝ², J. Amer. Math. Soc. 18 (2005) 313 MR2137980
58	D Mumford, Towards an enumerative geometry of the moduli space of curves, from: "Arithmetic and geometry, II" (editors M Artin, J Tate), Progr. Math. 36, Birkhäuser, Boston (1983) 271 MR717614
59	A Neitzke, Comparing signs in wall-crossing formulas, expository note (2016)
60	T Nishinou, B Siebert, Toric degenerations of toric varieties and tropical curves, Duke Math. J. 135 (2006) 1 MR2259922
61	H Ooguri, C Vafa, Knot invariants and topological strings, Nuclear Phys. B 577 (2000) 419 MR1765411
62	R Pandharipande, A Pixton, Descendent theory for stable pairs on toric 3–folds, J. Math. Soc. Japan 65 (2013) 1337 MR3127827
63	M Reineke, Poisson automorphisms and quiver moduli, J. Inst. Math. Jussieu 9 (2010) 653 MR2650811
64	M Reineke, Cohomology of quiver moduli, functional equations, and integrality of Donaldson–Thomas type invariants, Compos. Math. 147 (2011) 943 MR2801406
65	M Reineke, J Stoppa, T Weist, MPS degeneration formula for quiver moduli and refined GW/Kronecker correspondence, Geom. Topol. 16 (2012) 2097 MR3033514
66	M Reineke, T Weist, Refined GW/Kronecker correspondence, Math. Ann. 355 (2013) 17 MR3004575
67	Y Soibelman, On non-commutative analytic spaces over non-Archimedean fields, from: "Homological mirror symmetry" (editors A Kapustin, M Kreuzer, K G Schlesinger), Lecture Notes in Phys. 757, Springer (2009) 221 MR2596639
68	A Strominger, S T Yau, E Zaslow, Mirror symmetry is T–duality, Nuclear Phys. B 479 (1996) 243 MR1429831
69	Y Toda, Stability conditions and curve counting invariants on Calabi–Yau 3–folds, Kyoto J. Math. 52 (2012) 1 MR2892766
70	E Witten, Chern–Simons gauge theory as a string theory, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser, Basel (1995) 637 MR1362846
71	D Zagier, The dilogarithm function, from: "Frontiers in number theory, physics, and geometry, II" (editors P Cartier, B Julia, P Moussa, P Vanhove), Springer (2007) 3 MR2290758
72	E Zaslow, Wavefunctions for a class of branes in three-space, preprint (2018) arXiv:1803.02462