1.
Abramovich, D., Chen, Q.: Stable logarithmic maps to Deligne-Faltings pairs II. Asian J. Math.
18(3), 465–488 (2014)
MathSciNetCrossRefMATH
2.
Allermann, L., Rau, J.: First steps in tropical intersection theory. Mathematische zeitschrift
264(3), 633–670 (2010)
MathSciNetCrossRefMATH
3.
Auroux, D.: Mirror symmetry and T-duality in the complement of an anticanonical divisor. J. Gökova Geometry Topology
1, 51–91
4.
Barannikov, S.: Semi-infinite hodge structures and mirror symmetry for projective spaces. arXiv preprint math/0010157 (2000)
5.
Batyrev, V.V., Borisov, L.A.: On Calabi-Yau complete intersections in toric varieties. In: Higher-Dimensional Complex Varieties, Trento, 1994, pp. 39–65 (1996)
MathSciNetMATH
6.
Boehm, J., Bringmann, K., Buchholz, A., Markwig, H.: Tropical mirror symmetry for elliptic curves. arXiv preprint arXiv:1309.5893 (2013)
7.
Chen, Q.: Stable logarithmic maps to Deligne-Faltings pairs I. Ann. Math.
180(2), 455–521 (2014)
CrossRefMathSciNetMATH
8.
Fukaya, K.: Multivalued morse theory, asymptotic analysis and mirror symmetry. Graphs Patterns Math. Theor. Phys.
73, 205–278 (2005)
MathSciNetCrossRefMATH
9.
Fukaya, K., Oh, Y.-G., Ohta, H., Ono, K.: Lagrangian Floer theory on compact toric manifolds II: bulk deformations. Sel. Math.
17(3), 609–711 (2011)
MathSciNetCrossRefMATH
10.
Fulton, W.: Introduction to toric varieties, vol. 131. Princeton University Press, Princeton (1993)
MATH
11.
Gathmann, A.: Tropical algebraic geometry. Jahresbericht der DMV
108(1), 3–32
12.
Gathmann, A., Kerber, M., Markwig, H.: Tropical fans and the moduli spaces of tropical curves. Compos. Math.
145(01), 173–195 (2009)
MathSciNetCrossRefMATH
13.
Givental, A.B.: Equivariant Gromov-Witten invariants. Int. Math. Res. Not.
1996(13), 613–663 (1996)
MathSciNetCrossRefMATH
14.
Gross, M.: Toric degenerations and Batyrev-Borisov duality. Math. Ann.
333(3), 645–688 (2005)
MathSciNetCrossRefMATH
15.
Gross, M.: Mirror symmetry for
\(\mathbb{P}^{2}\) and tropical geometry. Adv. Math.
224(1), 169–245 (2010)
MathSciNetCrossRefMATH
16.
Gross, M.: Tropical Geometry and Mirror Symmetry, Volume 114 of CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, Washington, DC (2011)
17.
Gross, M.: Mirror symmetry and the Strominger-Yau-Zaslow conjecture. In: Current Developments in Mathematics. Intl. Press, Boston
18.
Gross, M., Siebert, B.: Affine manifolds, log structures, and mirror symmetry. Turk. J. Math.
27, 33–60 (2003)
MathSciNetMATH
19.
Gross, M., Siebert, B.: Mirror symmetry via logarithmic degeneration data, II. J. Algebr. Geom.
19(4), 679–780 (2010)
MathSciNetCrossRefMATH
20.
Gross, M., Siebert, B.: From real affine geometry to complex geometry. Ann. Math.
174(3), 1301–1428 (2011)
MathSciNetCrossRefMATH
21.
Gross, M., Siebert, B.: Logarithmic Gromov-Witten invariants. J. Am. Math. Soc.
26(2), 451–510 (2013)
MathSciNetCrossRefMATH
22.
Gross, M., Siebert, B., et al.: Mirror symmetry via logarithmic degeneration data I. J. Differ. Geom.
72(2), 169–338 (2006)
23.
Gross, M., Wilson, P.M.H., et al. Large complex structure limits of K3 surfaces. J. Differ. Geom.
55(3), 475–546 (2000)
24.
Hitchin, N.: The moduli space of special Lagrangian submanifolds. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze
25(3–4), 503–515 (1997)
MathSciNetMATH
25.
Illusie, L.: Logarithmic spaces (according to K. Kato), volume 15 of perspectives in mathematics. In: Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991). Academic, San Diego (1994)
26.
Iritani, H.: Quantum D-modules and generalized mirror transformations. Topology
47(4), 225–276 (2008)
MathSciNetCrossRefMATH
27.
Itenberg, I., Kharlamov, V., Shustin, E.: Welschinger invariant and enumeration of real rational curves. Int. Math. Res. Not.
2003(49), 2639–2653 (2003)
MathSciNetCrossRefMATH
28.
Kato, F.: Log smooth deformation and moduli of log smooth curves. Int. J. Math
11(2), 215–232 (2000)
CrossRefMathSciNetMATH
29.
Kato, K.: Logarithmic structures of Fontaine-Illusie. In: Algebraic Analysis, Geometry, and Number Theory, Baltimore, 1988. Johns Hopkins University Press, Baltimore (1989)
30.
Konishi, Y., Minabe, S.: Local B-model and mixed Hodge structure. Adv. Theor. Math. Phys.
14(4), 1089–1145 (2010)
MathSciNetCrossRefMATH
32.
Kontsevich, M., Soibelman, Y.: Affine structures and non-Archimedean analytic spaces. In: The Unity of Mathematics, pp. 321–385. Springer, New York (2006)
33.
Kontsevich, M., Soibelman, Y.: Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and mirror symmetry. arXiv preprint arXiv:1303.3253 (2013)
34.
Li, J.: Stable morphisms to singular schemes and relative stable morphisms. J. Differ. Geom.
57(3), 509–578 (2001)
MathSciNetMATH
35.
Manin, IU I.: Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces, vol. 47. American Mathematical Society, Providence (1999)
MATH
36.
Markwig, H., Rau, J.: Tropical descendant Gromov-Witten invariants. Manuscr. Math.
129(3), 293–335 (2009)
MathSciNetCrossRefMATH
37.
Mikhalkin, G.: Amoebas of algebraic varieties and tropical geometry. In: Different Faces of Geometry, pp. 257–300. Springer, New York (2004)
38.
Mikhalkin, G.: Enumerative tropical algebraic geometry in
\(\mathbb{R}^{2}\). J. Am. Math. Soc.
18(2), 313–377 (2005)
MathSciNetCrossRefMATH
39.
Milne, J.: Étale Cohomology. Volume 33 of Princeton Mathematical Series. Princeton University Press, Princeton (1980)
40.
Nishinou, T.: Disc counting on toric varieties via tropical curves. arXiv preprint math/0610660 (2006)
41.
Nishinou, T., Siebert, B.: Toric degenerations of toric varieties and tropical curves. Duke Math. J.
135(1), 1–51 (2006)
MathSciNetCrossRefMATH
42.
Ruddat, H.: Log Hodge groups on a toric Calabi-Yau degeneration. Mirror Symmetry Trop. Geom. Contemp. Math.
527, 113–164 (2008)
MathSciNetCrossRefMATH
43.
Ruddat, H., Siebert, B.: Canonical coordinates in toric degenerations (2014)
44.
Shustin, E.: A tropical calculation of the Welschinger invariants of real toric Del Pezzo surfaces. arXiv preprint math/0406099 (2004)
45.
Steenbrink, J.: Limits of Hodge structures. Invent. Math.
31(3), 229–257 (1975/1976)
46.
Strominger, A., Yau, S.-T., Zaslow, E.: Mirror symmetry is T-duality. Nucl. Phys. B
479(1), 243–259 (1996)
MathSciNetCrossRefMATH
47.
Welschinger, J.-Y.: Invariants of real rational symplectic 4-manifolds and lower bounds in real enumerative geometry. C. R. Math. Acad. Sci. Paris
336(4), 341–344 (2003)
MathSciNetCrossRefMATH
