Geometry & Topology Volume 18, issue 3 (2014)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Conifold transitions via affine geometry and mirror symmetry

Ricardo Castaño-Bernard and Diego Matessi

Geometry & Topology 18 (2014) 1769–1863

DOI: 10.2140/gt.2014.18.1769

Bibliography

1	P S Aspinwall, T Bridgeland, A Craw, M R Douglas, M Gross, A Kapustin, G W Moore, G Segal, B Szendrői, P M H Wilson, Dirichlet branes and mirror symmetry, 4, Amer. Math. Soc. (2009) MR2567952
2	V V Batyrev, L A Borisov, Mirror duality and string-theoretic Hodge numbers, Invent. Math. 126 (1996) 183 MR1408560
3	V V Batyrev, I Ciocan-Fontanine, B Kim, D van Straten, Conifold transitions and mirror symmetry for Calabi–Yau complete intersections in Grassmannians, Nuclear Phys. B 514 (1998) 640 MR1619529
4	R Castaño Bernard, D Matessi, Lagrangian 3–torus fibrations, J. Differential Geom. 81 (2009) 483 MR2487600
5	R Friedman, On threefolds with trivial canonical bundle, from: "Complex geometry and Lie theory" (editors J A Carlson, C H Clemens, D R Morrison), Proc. Sympos. Pure Math. 53, Amer. Math. Soc. (1991) 103 MR1141199
6	E Goldstein, Calibrated fibrations on noncompact manifolds via group actions, Duke Math. J. 110 (2001) 309 MR1865243
7	M Gross, Examples of special Lagrangian fibrations, from: "Symplectic geometry and mirror symmetry" (editors K Fukaya, Y G Oh, K Ono, G Tian), World Sci. Publ. (2001) 81 MR1882328
8	M Gross, Topological mirror symmetry, Invent. Math. 144 (2001) 75 MR1821145
9	M Gross, Toric degenerations and Batyrev–Borisov duality, Math. Ann. 333 (2005) 645 MR2198802
10	M Gross, The Strominger–Yau–Zaslow conjecture : from torus fibrations to degenerations, from: "Algebraic geometry—Seattle 2005, Part 1" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 149 MR2483935
11	M Gross, B Siebert, Mirror symmetry via logarithmic degeneration data, I, J. Differential Geom. 72 (2006) 169 MR2213573
12	M Gross, B Siebert, Mirror symmetry via logarithmic degeneration data, II, J. Algebraic Geom. 19 (2010) 679 MR2669728
13	M Gross, B Siebert, From real affine geometry to complex geometry, Ann. of Math. 174 (2011) 1301 MR2846484
14	M Gross, P M H Wilson, Large complex structure limits of K3 surfaces, J. Differential Geom. 55 (2000) 475 MR1863732
15	C Haase, I Zharkov, Integral affine structures on spheres and torus fibrations of Calabi–Yau toric hypersurfaces, I, arXiv:math.AG/0205321
16	C Haase, I Zharkov, Integral affine structures on spheres and torus fibrations of Calabi–Yau toric hypersurfaces, II, arXiv:math.AG/0301222
17	C Haase, I Zharkov, Integral affine structures on spheres: complete intersections, Int. Math. Res. Not. 2005 (2005) 3153 MR2187503
18	N J Hitchin, The moduli space of special Lagrangian submanifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 (1997) 503 MR1655530
19	S Hosono, M H Saito, J Stienstra, On the mirror symmetry conjecture for Schoen’s Calabi–Yau 3–folds, from: "Integrable systems and algebraic geometry" (editors M H Saito, Y Shimizu, K Ueno), World Sci. Publ. (1998) 194 MR1672045
20	M Kontsevich, Y Soibelman, Homological mirror symmetry and torus fibrations, from: "Symplectic geometry and mirror symmetry" (editors K Fukaya, Y G Oh, K Ono, G Tian), World Sci. Publ. (2001) 203 MR1882331
21	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
22	P Lu, G Tian, The complex structure on a connected sum of S³ × S³ with trivial canonical bundle, Math. Ann. 298 (1994) 761 MR1268603
23	G Mikhalkin, Introduction to Tropical Geometry, arXiv:0709.1049
24	G Mikhalkin, Decomposition into pairs-of-pants for complex algebraic hypersurfaces, Topology 43 (2004) 1035 MR2079993
25	D R Morrison, Through the looking glass, from: "Mirror symmetry, III" (editors D H Phong, L Vinet, S T Yau), AMS/IP Stud. Adv. Math. 10, Amer. Math. Soc. (1999) 263 MR1673108
26	M Rossi, Geometric transitions, J. Geom. Phys. 56 (2006) 1940 MR2240431
27	W D Ruan, Lagrangian torus fibrations and mirror symmetry of Calabi–Yau manifolds, from: "Symplectic geometry and mirror symmetry" (editors K Fukaya, Y G Oh, K Ono, G Tian), World Sci. Publ. (2001) 385 MR1882335
28	W D Ruan, Newton polygon and string diagram, Comm. Anal. Geom. 15 (2007) 77 MR2301249
29	C Schoen, On fiber products of rational elliptic surfaces with section, Math. Z. 197 (1988) 177 MR923487
30	I Smith, R P Thomas, S T Yau, Symplectic conifold transitions, J. Differential Geom. 62 (2002) 209 MR1988503
31	A Strominger, S T Yau, E Zaslow, Mirror symmetry is T–duality, Nuclear Phys. B 479 (1996) 243 MR1429831
32	G Tian, Smoothing 3–folds with trivial canonical bundle and ordinary double points, from: "Essays on mirror manifolds" (editor S T Yau), Int. Press, Hong Kong (1992) 458 MR1191437