References
Borisov, L.: Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties. Preprint, 1993, alg-geom/9310001
Batyrev, V., Borisov, L.: On Calabi-Yau complete intersections in toric varieties. In: Higher-dimensional complex varieties (Trento, 1994), de Gruyter, Berlin, 1996, pp. 39–65
Gross, M., Siebert, B.: Affine manifolds, log structures, and mirror symmetry. Turkish J. Math. 27, 33–60 (2003)
Gross, M., Siebert, B.: Mirror Symmetry via Logarithmic Degeneration Data I. Preprint, 2003 math.AG/0309070, Third Version
Gross, M., Siebert, B.: Torus fibrations and toric degenerations. In preparation
Haase, C., Zharkov, I.: Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces I. preprint, 2002, math.AG/0205321
Haase, C., Zharkov, I.: Integral affine structures on spheres III: complete intersections. Preprint, 2005, math.AG/0504181
Hosono, S., Saito, M-H., Stienstra, J.: On the mirror symmetry conjecture for Schoen's Calabi-Yau 3-folds. In: Integrable systems and algebraic geometry (Kobe/Kyoto, 1997), World Sci. Publishing, River Edge, NJ, 1998, pp. 194–235
Hu, S.: Semi-stable Degeneration of Toric Varieties and their hypersurfaces. Preprint, 2001, math.AG/0110091
Kovalev, A.: IPAM lecture, April 2003
Leung, N.-C, Symington, M.: Almost toric symplectic four-manifolds. Preprint, 2003, math.SG/0312165
Matsumura, H.: Commutative algebra. Second edition. Mathematics Lecture Note Series, 56. Benjamin/Cummings Publishing Co., Inc., Reading, Mass., 1980
Oda, T.: Convex bodies and algebraic geometry. An introduction to the theory of toric varieties. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 15. Springer-Verlag, Berlin, 1988
Ruan, W.-D.: Lagrangian torus fibration and mirror symmetry of Calabi-Yau hypersurface in toric variety. Preprint, 2000, math.DG/0007028
Schoen, C.: On fiber products of rational elliptic surfaces with section. Math. Z. 197, 177–199 (1988)
Strominger, A., Yau, S.-T., Zaslow, E.: Mirror Symmetry is T-Duality. Nucl. Phys. B479, 243–259 (1996)
Zharkov, I.: Torus fibrations of Calabi-Yau hypersurfaces in toric varieties. Duke Math. J. 101, 237–257 (2000)
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This work was partially supported by NSF grant 0204326.
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Gross, M. Toric degenerations and Batyrev-Borisov duality. Math. Ann. 333, 645–688 (2005). https://doi.org/10.1007/s00208-005-0686-7
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DOI: https://doi.org/10.1007/s00208-005-0686-7