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

Volume 27
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 higher-dimensional tropical vertex

Hülya Argüz and Mark Gross

Geometry & Topology 26 (2022) 2135–2235
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, Compos. Math. 156 (2020) 2020 MR4177284
3 D Abramovich, Q Chen, M Gross, B Siebert, Punctured logarithmic maps, preprint (2020) arXiv:2009.07720
4 D Abramovich, Q Chen, S Marcus, M Ulirsch, J Wise, Skeletons and fans of logarithmic structures, from: "Nonarchimedean and tropical geometry" (editors M Baker, S Payne), Springer (2016) 287 MR3702314
5 D Abramovich, Q Chen, S Marcus, J Wise, Boundedness of the space of stable logarithmic maps, J. Eur. Math. Soc. 19 (2017) 2783 MR3692887
6 H Argüz, Equations of mirrors to log Calabi–Yau pairs via the heart of canonical wall structures, preprint (2021) arXiv:2109.08664
7 H Argüz, P Bousseau, The flow tree formula for Donaldson–Thomas invariants of quivers with potentials, preprint (2021) arXiv:2102.11200
8 H Argüz, T Prince, Real Lagrangians in Calabi–Yau threefolds, Proc. Lond. Math. Soc. 121 (2020) 287 MR4093957
9 P Bousseau, The quantum tropical vertex, Geom. Topol. 24 (2020) 1297 MR4157555
10 M W Cheung, T Mandel, Donaldson–Thomas invariants from tropical disks, Selecta Math. 26 (2020) MR4131036
11 R Donagi, S Katz, M Wijnholt, Weak coupling, degeneration and log Calabi–Yau spaces, Pure Appl. Math. Q. 9 (2013) 655 MR3263972
12 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
13 W M Goldman, Geometric structures on manifolds, preprint (2021)
14 W Goldman, M W Hirsch, The radiance obstruction and parallel forms on affine manifolds, Trans. Amer. Math. Soc. 286 (1984) 629 MR760977
15 M Gross, P Hacking, S Keel, Mirror symmetry for log Calabi–Yau surfaces, I, Publ. Math. Inst. Hautes Études Sci. 122 (2015) 65 MR3415066
16 M Gross, P Hacking, S Keel, M Kontsevich, Canonical bases for cluster algebras, J. Amer. Math. Soc. 31 (2018) 497 MR3758151
17 M Gross, P Hacking, B Siebert, Theta functions on varieties with effective anti-canonical class, 1367, Amer. Math. Soc. (2022) MR4426709
18 M Gross, R Pandharipande, B Siebert, The tropical vertex, Duke Math. J. 153 (2010) 297 MR2667135
19 M Gross, B Siebert, From real affine geometry to complex geometry, Ann. of Math. 174 (2011) 1301 MR2846484
20 M Gross, B Siebert, Logarithmic Gromov–Witten invariants, J. Amer. Math. Soc. 26 (2013) 451 MR3011419
21 M Gross, B Siebert, Local mirror symmetry in the tropics, from: "Proceedings of the International Congress of Mathematicians, II" (editors S Y Jang, Y R Kim, D W Lee, I Ye), Kyung Moon Sa (2014) 723 MR3728635
22 M Gross, B Siebert, Intrinsic mirror symmetry and punctured Gromov–Witten invariants, from: "Algebraic geometry" (editors T de Fernex, B Hassett, M Mustaţă, M Olsson, M Popa, R Thomas), Proc. Sympos. Pure Math. 97, Amer. Math. Soc. (2018) 199 MR3821173
23 M Gross, B Siebert, Intrinsic mirror symmetry, preprint (2019) arXiv:1909.07649
24 M Gross, B Siebert, The canonical wall structure and intrinsic mirror symmetry, Invent. Math. 229 (2022) 1101 MR4462625
25 E N Ionel, T H Parker, Relative Gromov–Witten invariants, Ann. of Math. 157 (2003) 45 MR1954264
26 S Keel, T Y Yu, The Frobenius structure theorem for affine log Calabi–Yau varieties containing a torus, preprint (2019) arXiv:1908.09861
27 J Kollár, C Xu, The dual complex of Calabi–Yau pairs, Invent. Math. 205 (2016) 527 MR3539921
28 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 (2006) 321 MR2181810
29 A M Li, Y Ruan, Symplectic surgery and Gromov–Witten invariants of Calabi–Yau 3–folds, Invent. Math. 145 (2001) 151 MR1839289
30 J Li, Stable morphisms to singular schemes and relative stable morphisms, J. Differential Geom. 57 (2001) 509 MR1882667
31 T Mandel, Scattering diagrams, theta functions, and refined tropical curve counts, J. Lond. Math. Soc. 104 (2021) 2299
32 T Mandel, Theta bases and log Gromov–Witten invariants of cluster varieties, Trans. Amer. Math. Soc. 374 (2021) 5433 MR4293777
33 C Manolache, Virtual pull-backs, J. Algebraic Geom. 21 (2012) 201 MR2877433
34 J Nicaise, C Xu, T Y Yu, The non-archimedean SYZ fibration, Compos. Math. 155 (2019) 953 MR3946280
35 T Oda, Convex bodies and algebraic geometry: an introduction to the theory of toric varieties, 15, Springer (1988) MR922894
36 A Ogus, Lectures on logarithmic algebraic geometry, 178, Cambridge Univ. Press (2018) MR3838359
37 M C Olsson, Logarithmic geometry and algebraic stacks, Ann. Sci. École Norm. Sup. 36 (2003) 747 MR2032986
38 B Parker, Tropical enumeration of curves in blowups of the projective plane, preprint (2014) arXiv:1411.5722
39 J Pascaleff, On the symplectic cohomology of log Calabi–Yau surfaces, Geom. Topol. 23 (2019) 2701 MR4039179
40 A Strominger, S T Yau, E Zaslow, Mirror symmetry is T–duality, Nuclear Phys. B 479 (1996) 243 MR1429831
41 N Takahashi, Log mirror symmetry and local mirror symmetry, Comm. Math. Phys. 220 (2001) 293 MR1844627
42 T Y Yu, Enumeration of holomorphic cylinders in log Calabi–Yau surfaces, I, Math. Ann. 366 (2016) 1649 MR3563248