Special Lagrangian Fibrations, Mirror Symmetry and Calabi-Yau Double Covers
Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon, Astérisque, no. 321 (2008), pp. 99-128.
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Auroux, Denis. Special Lagrangian Fibrations, Mirror Symmetry and Calabi-Yau Double Covers, dans Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon, Astérisque, no. 321 (2008), pp. 99-128. http://archive.numdam.org/item/AST_2008__321__99_0/

[1] M. Abouzaid - "Morse homology, tropical geometry, and homological mirror symmetry for toric varieties", preprint arXiv:math.SG/0610004. | DOI | MR | Zbl

[2] M. Abouzaid, D. Auroux & L. Katzarkov - in preparation.

[3] D. Auroux - "Mirror symmetry and T-duality in the complement of an anticanonical divisor", J. Gökova Geom. Topol. GGT 1 (2007), p. 51-91. | MR | Zbl

[4] D. Auroux, L. Katzarkov & D. Orlov - "Mirror symmetry for del Pezzo surfaces: vanishing cycles and coherent sheaves", Invent. Math. 166 (2006), p. 537-582. | DOI | MR | Zbl

[5] C.-H. Cho & Y.-G. Oh - "Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds", Asian J. Math. 10 (2006), p. 773-814. | DOI | MR | Zbl

[6] K. Fukaya, Y.-G. Oh, H. Ohta & K. Ono - "Lagrangian intersection Floer theory: Anomaly and obstruction", preprint, second expanded version, 2006. | MR | Zbl

[7] K. Fukaya, Y.-G. Oh, H. Ohta & K. Ono, "Lagrangian Floer theory on compact toric manifolds I", preprint arXiv:0802.1703. | MR | Zbl

[8] M. Gross - "Special Lagrangian fibrations. II. Geometry. A survey of techniques in the study of special Lagrangian fibrations", in Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds (Cambridge, MA, 1999), AMS/IP Stud. Adv. Math., vol. 23, Amer. Math. Soc., 2001, p. 95-150. | DOI | MR | Zbl

[9] M. Gross & B. Siebert - "Affine manifolds, log structures, and mirror symmetry", Turkish J. Math. 27 (2003), p. 33-60. | MR | Zbl

[10] M. Gross & B. Siebert, "From real affine geometry to complex geometry", preprint arXiv:math.AG/0703822. | DOI | MR | Zbl

[11] N. J. Hitchin - "The moduli space of special Lagrangian submanifolds", Ann. Scuola Norm. Sup. Pisa CI. Sci. 25 (1997) | EuDML | Numdam | MR | Zbl

N. J. Hitchin - "The moduli space of special Lagrangian submanifolds", Ann. Scuola Norm. Sup. Pisa CI. Sci. 25, p. 503-515 (1998). | EuDML | Numdam | MR | Zbl

[12] K. Hori - "Mirror symmetry and quantum geometry", in Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002), Higher Ed. Press, 2002, p. 431-443. | MR | Zbl

[13] K. Hori, A. Iqbal & C. Vafa - "D-branes and mirror symmetry", preprint arXivrhep-th/0005247.

[14] K. Hori & C. Vafa - "Mirror symmetry", preprint arXiv:hep-th/0002222. | Zbl

[15] D. Huybrechts - "Moduli spaces of hyperkähler manifolds and mirror symmetry", in Intersection theory and moduli, ICTP Lect. Notes, XIX, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2004, p. 185-247. | MR | Zbl

[16] D. Joyce - "Special Lagrangian submanifolds with isolated conical singularities. V. Survey and applications", J. Differential Geom. 63 (2003), p. 279-347. | DOI | MR | Zbl

[17] D. Joyce, "Lectures on Calabi-Yau and special Lagrangian geometry", preprint arXiv:math.DG/0108088.

[18] A. Kapustin & Y. Li - "D-branes in Landau-Ginzburg models and algebraic geometry", J. High Energy Phys. 12 (2003). | MR

[19] M. Kontsevich - "Homological algebra of mirror symmetry", in Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Birkhäuser, 1995, p. 120-139. | DOI | MR | Zbl

[20] M. Kontsevich, "Lectures at ENS, Paris, Spring 1998", notes taken by J. Bellaiche, J.-F. Dat, I. Marin, G. Racinet and H. Randriambololona, unpublished.

[21] M. Kontsevich & Y. Soibelman - "Affine structures and non-Archimedean analytic spaces", in The unity of mathematics, Progr. Math., vol. 244, Birkhäuser, 2006, p. 321-385. | DOI | MR | Zbl

[22] N. C. Leung - "Mirror symmetry without corrections", preprint arXiv:math.DG/0009235. | MR | Zbl

[23] R. C. Mclean - "Deformations of calibrated submanifolds", Comm. Anal. Geom. 6 (1998), p. 705-747. | DOI | MR | Zbl

[24] D. Orlov - "Triangulated categories of singularities and D-branes in Landau-Ginzburg models", preprint arXiv:math.AG/0302304. | Zbl

[25] A. Polishchuk & E. Zaslow - "Categorical mirror symmetry: the elliptic curve", Adv. Theor. Math. Phys. 2 (1998), p. 443-470. | DOI | MR | Zbl

[26] P. Seidel - "Vanishing cycles and mutation", in European Congress of Mathematics, Vol. II (Barcelona, 2000), Progr. Math., vol. 202, Birkhäuser, 2001, p. 65-85. | DOI | MR | Zbl

[27] P. Seidel, Fukaya categories and Picard-Lefschetz theory, Zurich Lectures in Advanced Mathematics, European Mathematical Society (EMS), Zürich, 2008. | DOI | MR | Zbl

[28] A. Strominger, S.-T. Yau & E. Zaslow - "Mirror symmetry is T-duality", Nuclear Phys. B 479 (1996), p. 243-259. | DOI | MR | Zbl

[29] M. Symington - "Four dimensions from two in symplectic topology", in Topology and geometry of manifolds (Athens, GA, 2001), Proc. Sympos. Pure Math., vol. 71, Amer. Math. Soc., 2003, p. 153-208. | DOI | MR | Zbl