Volume 24, issue 3 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 27
Issue 8, 2937–3385
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
The quantum tropical vertex

Pierrick Bousseau

Geometry & Topology 24 (2020) 1297–1379
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 23 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 2, 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 2, 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