Fetching the paper…
Reading the bibliography…
We formulate some precise conjectures concerning the existence and structure of supersymmetric T3 fibrations of Calabi-Yau threefolds, and describe how these conjectural fibrations would give rise to the Strominger-Yau-Zaslow version of mirror symmetry.
E. Calabi, On Kähler manifolds with vanishing canonical class , Algebraic Geometry and Topology, A Symposium in Honor of S. Lefschetz (R. H. Fox et al., eds.), Princeton University Press, Princeton, 1957, pp. 78–89
1957
Earlier work this paper cites.
K. Kodaira, On compact analytic surfaces. II, III , Ann. of Math. (2) 77
1963
Earlier work this paper cites.
S.-T. Yau, Calabi’s conjecture and some new results in algebraic geometry , Proc. Nat. Acad. Sci. U.S.A. 74
1977
Earlier work this paper cites.
A. G. Khovanskiĭ, Newton polyhedra, and the genus of complete intersections , Funktsional. Anal. i Prilozhen. 12
1978
Earlier work this paper cites.
M. Gromov, Structures métriques pour les variétés riemanniennes , Textes Mathématiques, vol. 1, CEDIC, Paris, 1981, edited by J. Lafontaine and P. Pansu
1981
Earlier work this paper cites.
R. Harvey and H. B. Lawson, Jr., Calibrated geometries , Acta Math. 148
1982
Earlier work this paper cites.
P. Candelas, A. M. Dale, C. A. Lütken, and R. Schimmrigk, Complete intersection Calabi–Yau manifolds , Nuclear Phys. B 298
1988
Earlier work this paper cites.
P. S. Aspinwall, C. A. Lütken, and G. G. Ross, Construction and couplings of mirror manifolds , Phys. Lett. B 241
1990
Earlier work this paper cites.
P. Candelas, M. Lynker, and R. Schimmrigk, Calabi–Yau manifolds in weighted ℙ 4 \mathbb{P}_{4} , Nuclear Phys. B 341
1990
Earlier work this paper cites.
B. R. Greene and M. R. Plesser, Duality in Calabi–Yau moduli space , Nuclear Phys. B 338
1990
Earlier work this paper cites.
P. Candelas, X. C. de la Ossa, P. S. Green, and L. Parkes, A pair of Calabi–Yau manifolds as an exactly soluble superconformal theory , Nuclear Phys. B 359
1991
Earlier work this paper cites.
A. Ceresole, R. D’Auria, S. Ferrara, W. Lerche, and J. Louis, Picard–Fuchs equations and special geometry , Int. J. Mod. Phys. A 8
1993
Earlier work this paper cites.
D. R. Morrison, Mirror symmetry and rational curves on quintic threefolds: A guide for mathematicians , J. Amer. Math. Soc. 6
1993
Earlier work this paper cites.
by same author, Compactifications of moduli spaces inspired by mirror symmetry , Journées de Géométrie Algébrique d’Orsay (Juillet 1992), Astérisque, vol. 218, Société Mathématique de France, 1993, pp. 243–271, arXiv:alg-geom/9304007
1993
Earlier work this paper cites.
E. Witten, Phases of N = 2 N=2 theories in two dimensions , Nuclear Phys. B 403
1993
Earlier work this paper cites.
P. S. Aspinwall, B. R. Greene, and D. R. Morrison, Calabi–Yau moduli space, mirror manifolds and spacetime topology change in string theory , Nuclear Phys. B 416
1994
Earlier work this paper cites.
V. V. Batyrev, Dual polyhedra and mirror symmetry for Calabi–Yau hypersurfaces in toric varieties , J. Algebraic Geom. 3
1994
Earlier work this paper cites.
P. Candelas, X. de la Ossa, A. Font, S. Katz, and D. R. Morrison, Mirror symmetry for two parameter models – I , Nuclear Phys. B 416
1994
Earlier work this paper cites.
I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, resultants and multidimensional determinants , Birkhäuser Boston, 1994
1994
Earlier work this paper cites.
B. R. Greene, D. R. Morrison, and A. Strominger, Black hole condensation and the unification of string vacua , Nuclear Phys. B 451
1995
Earlier work this paper cites.
S. Hosono, A. Klemm, S. Theisen, and S.-T. Yau, Mirror symmetry, mirror map and applications to Calabi–Yau hypersurfaces , Commun. Math. Phys. 167
1995
Earlier work this paper cites.
V. V. Batyrev and L. A. Borisov, On Calabi–Yau complete intersections in toric varieties , Higher-dimensional complex varieties (Trento, 1994), de Gruyter, Berlin, 1996, pp. 39–65, arXiv:alg-geom/9412017
1996
Earlier work this paper cites.
by same author, Beyond the Kähler cone , Proc. of the Hirzebruch 65 Conference on Algebraic Geometry (M. Teicher, ed.), Israel Math. Conf. Proc., vol. 9, Bar-Ilan University, 1996, pp. 361–376, arXiv:alg-geom/9407007
1996
Earlier work this paper cites.
A. Strominger, S.-T. Yau, and E. Zaslow, Mirror symmetry is T-duality , Nuclear Phys. B 479
1996
Earlier work this paper cites.
P. S. Aspinwall and D. R. Morrison, String theory on K3 surfaces , Mirror Symmetry II (B. Greene and S.-T. Yau, eds.), International Press, Cambridge, 1997, pp. 703–716, arXiv:hep-th/9404151
1997
Cited alongside, same era.
P. Deligne, Local behavior of Hodge structures at infinity , Mirror symmetry, II, AMS/IP Stud. Adv. Math., vol. 1, Amer. Math. Soc., 1997, pp. 683–699
1997
Cited alongside, same era.
M. Gross and P. M. H. Wilson, Mirror symmetry via 3 3 -tori for a class of Calabi–Yau threefolds , Math. Ann. 309
1997
Cited alongside, same era.
N. Hitchin, The moduli space of special Lagrangian submanifolds , Annali Scuola Sup. Norm. Pisa Sci. Fis. Mat. 25
1997
Cited alongside, same era.
M. Gross, Special Lagrangian fibrations. I. Topology , Integrable systems and algebraic geometry (Kobe/Kyoto, 1997), World Sci. Publishing, River Edge, NJ, 1998, pp. 156–193, arXiv:alg-geom/9710006
M. Gross, D. Huybrechts, and D. Joyce, Calabi–Yau manifolds and related geometries. Lectures from the summer school held in Nordfjordeid, June 2001 , Springer-Verlag, 2003
2003
Later among the works it cites.
M. Gross and B. Siebert, Affine manifolds, log structures, and mirror symmetry , Turkish J. Math. 27
2003
Later among the works it cites.
K. Hori, S. Katz, A. Klemm, R. Pandharipande, R. Thomas, C. Vafa, R. Vakil, and E. Zaslow, Mirror symmetry , Clay Mathematics Monographs, vol. 1, American Mathematical Society, Providence, RI, 2003
2003
Later among the works it cites.
D. Joyce, Singularities of special Lagrangian fibrations and the SYZ conjecture , Comm. Anal. Geom. 11
2003
Later among the works it cites.
by same author, Lagrangian torus fibration of quintic Calabi–Yau hypersurfaces. III. Symplectic topological SYZ mirror construction for general quintics , J. Differential Geom. 63
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
1998
Cited alongside, same era.
R. C. McLean, Deformations of calibrated submanifolds , Comm. Anal. Geom. 6
1998
Cited alongside, same era.
D. A. Cox and S. Katz, Mirror symmetry and algebraic geometry , Mathematical Surveys and Monographs, vol. 68, American Mathematical Society, Providence, RI, 1999
1999
Cited alongside, same era.
by same author, Special Lagrangian fibrations. II. Geometry. A survey of techniques in the study of special Lagrangian fibrations , Surveys in differential geometry: differential geometry inspired by string theory, Surv. Differ. Geom., vol. 5, International Press, Cambridge, 1999, pp. 341–403, arXiv:math.AG/9809072
1999
Cited alongside, same era.
by same author, The geometry underlying mirror symmetry , New Trends in Algebraic Geometry (K. Hulek, F. Catanese, C. Peters, and M. Reid, eds.), London Math. Soc. Lecture Notes, vol. 264, Cambridge University Press, 1999, pp. 283–310, arXiv:alg-geom/9608006
1999
Cited alongside, same era.
by same author, Through the looking glass , Mirror Symmetry III (D. H. Phong, L. Vinet, and S.-T. Yau, eds.), AMS/IP Studies in Advanced Mathematics, vol. 10, American Mathematical Society and International Press, 1999, pp. 263–277, arXiv:alg-geom/9705028
1999
Cited alongside, same era.
M. Forsberg, M. Passare, and A. Tsikh, Laurent determinants and arrangements of hyperplane amoebas , Adv. Math. 151
2000
Cited alongside, same era.
by same author, Large complex structure limits of K 3 K3 surfaces , J. Differential Geom. 55
2000
Cited alongside, same era.
2003
Later among the works it cites.
by same author, Amoebas of complex curves and tropical curves , UK-Japan Winter School 2004—Geometry and Analysis Towards Quantum Theory, Sem. Math. Sci., vol. 30, Keio Univ., 2004, pp. 24–36
2004
Later among the works it cites.
G. Mikhalkin, Amoebas of algebraic varieties and tropical geometry , Different faces of geometry, Int. Math. Ser., vol. 3, Kluwer/Plenum, New York, 2004, pp. 257–300, arXiv:math.AG/0403015
2004
Later among the works it cites.
M. Passare and H. Rullgård, Amoebas, Monge-Ampère measures, and triangulations of the Newton polytope , Duke Math. J. 121
2004
Later among the works it cites.
M. Aganagic, A. Klemm, M. Mariño, and C. Vafa, The topological vertex , Commun. Math. Phys. 254
2005
Later among the works it cites.
R. Castaño-Bernard and D. Matessi, Some piece-wise smooth Lagrangian fibrations , Rend. Semin. Mat. Univ. Politec. Torino 63
2005
Later among the works it cites.
by same author, Toric degenerations and Batyrev-Borisov duality , Math. Ann. 333
2005
Later among the works it cites.
by same author, Integral affine structures on spheres: complete intersections , Int. Math. Res. Not. (2005) 3153–3167, arXiv:math.AG/0504181
2005
Later among the works it cites.
by same author, U ( 1 ) \rm U(1) -invariant special Lagrangian 3-folds. I. Nonsingular solutions , Adv. Math. 192
2005
Later among the works it cites.
by same author, U ( 1 ) \rm U(1) -invariant special Lagrangian 3-folds. II. Existence of singular solutions , Adv. Math. 192
2005
Later among the works it cites.
by same author, U ( 1 ) \rm U(1) -invariant special Lagrangian 3-folds. III. Properties of singular solutions , Adv. Math. 192
2005
Later among the works it cites.
N. C. Leung, Mirror symmetry without corrections , Comm. Anal. Geom. 13
2005
Later among the works it cites.
by same author, Mirror symmetry via logarithmic degeneration data. I , J. Differential Geom. 72
2006
Later among the works it cites.
by same author, Affine structures and non-Archimedean analytic spaces , The unity of mathematics, Progr. Math., vol. 244, Birkhäuser Boston, 2006, pp. 321–385, arXiv:math.AG/0406564
2006
Later among the works it cites.
by same author, Newton polygon and string diagram , Comm. Anal. Geom. 15
2007
Later among the works it cites.
by same author, Generalized special Lagrangian torus fibration for Calabi–Yau hypersurfaces in toric varieties. I , Commun. Contemp. Math. 9
2007
Later among the works it cites.
by same author, Generalized special Lagrangian torus fibration for Calabi–Yau hypersurfaces in toric varieties II , Mirror Symmetry V (N. Yui, S.-T. Yau, and J. D. Lewis, eds.), American Mathematical Society and International Press, 2007, arXiv:math.DG/0303278
2007
Later among the works it cites.
by same author, Lagrangian 3-torus fibrations , J. Differential Geom. 81
2009
Later among the works it cites.