Large complex structure limits of K3 surfaces

Journal of Differential Geometry

Volumn 55, Issue 3, 2000, Pages 475-546

  Gross, Mark ^a   Wilson, P M H ^b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034215859     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1090341262     Document Type: Article

References (36)

1. 2 structure of moduli spaces of Einstein metrics on 4-manifolds, Geom. Funct. Anal. 2 (1992) 29-89.
2. M. Anderson, P. Kronheimer & C. Lebrun, Complete Ricci-flat Kahler manifolds of infinite topological type, Comm. Math. Phys. 125 (1989) 637-642.
3. M. Abramowitz & I. Stegun (eds.), Handbook of mathematical functions, Dover Publications, 1965.
4. P. Aspinwall & D. Morrison, String theory on K3 surfaces, Essays on Mirror Manifolds. II, (Greene, B.R., Yau, S.-T. eds.) Hong Kong, Internat. Press, 1996, 703-716.
5. W. Barth, C. Peters & A. van de Ven, Compact complex surfaces, Springer, 1984.
6. A. Besse, Einstein manifolds, Springer, 1987.
7. S. Y. Cheng & S.-T. Yau, On the existence of a complete Kãhler metric on non compact complex manifolds and the regularity of Fefferman’s equation, Comm. Pure Appl. Math. 33 (1980) 507-544.
8. S.-s. Chern, Complex manifolds without potential theory, 2nd edition, Springer, 1979.
9. C. Croke, Some isoperimetric inequalities and eigenvalue estimates, Ann. Sci. Ecole Norm. Sup. 13 (1980) 419-435.
10. I. Dolgachev, Mirror symmetry for lattice polarized K3 surfaces, Algebraic Ge-ometry, 4 J. Math. Sci. 81 (1996) 2599-2630.
11. D. Gilbarg & N. Trudinger, Elliptic partial differential equations of second order, 2ed., rev. 3. printing, Springer, 1998.
12. B. Greene, A. Shapere, C. Vafa & S.-T. Yau, Stringy cosmic strings and noncom-pact Calabi-Yau manifolds, Nucl. Phys. B 337 (1990) 1-36.
13. M. Gross, Special Lagrangian fibrations I: Topology, Integrable Systems and Algebraic Geometry, (eds. M.-H. Saito, Y. Shimizu and K. Ueno), World Scientific, 1998, 156-193.
14. M. Gross, Special Lagrangian fibrations II: Geometry, Surveys in Differential Geometry, Somerville, MA, Internat. Press, 1999, 341-403.
15. M. Gross, Topological mirror symmetry, Invent. Math. 144 (2001) 75-137.
16. M. Gross, Examples of special Lagrangian, fibrations, preprint, math.AG/0012002, (2000).
17. M. Gross & P. M. H. Wilson, Mirror symmetry via 3-torifor a class of Calabi-Yau threefolds, Math. Ann. 309 (1997) 505-531.
18. R. Harvey, & H. B. Lawson, Jr., Calibrated geometries, Acta Math. 148 (1982) 47-157.
19. N. Hitchin, The Moduli Space of Special Lagrangian Submanifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 (1997) 503-515.
20. R. Kobayashi, Moduli of Einstein metrics on a K3 surface and degeneration of type I, Kahler metric and moduli spaces, Adv. Stud. Pure Math., 18-II, Academic Press, 1990, 257-311.
21. R. Kobayashi & A. Todorov, Polarized period map for generalized K3 surfaces and the moduli of Einstein metrics, Tohoku Math. J. 39 (1987) 341-363.
22. M. Kontsevich & Y. Soibelman, Homological mirror symmetry and torus fibra-tions, preprint, math.SG/0011041, revised version, June 4, 2001.
23. P. Li, On the Sobolev constant and the p-spectrum of a compact Riemannian manifold, Ann. Sci. École Norm. Sup. 13 (1980) 451-468.
24. P. Lu, Kahler-Einstein metrics on Kummer threefold and special Lagrangian tori, Comm. Anal. Geom. 7 (1999) 787-806.
25. Yu. Manin, Moduli, motives, mirrors, preprint, math.AG/0005144.
26. R. C. McLean, Deformations of calibrated submanifolds, Comm. Anal. Geom. 6 (1998) 705-747.
27. D. Morrison, Compactifications of moduli spaces inspired by mirror symmetry, J. Geometrie Algebrique d’Orsay, Juillet 1992, Asterisque 218 (1993) 243-271.
28. S. Nergiz & C. Saclioglu, A quasiperiodic Gibbons-Hawking metric and spacetime foam, Phys. Rev. D (3) 53 (1996) 2240-2243.
29. H. Ooguri & C. Vafa, Summing up Dirichlet instantons, Phys. Rev. Lett. 77 (1996) 3296-3298.
30. P. Petersen, Riemannian geometry, Springer, 1997.
31. R. Schoen, & S.-T. Yau, Lectures on differential geometry, Conf. Proc. Lecture Notes in Geom. and Topology, Vol. I, Internat. Press, 1994.
32. A. Strominger, S.-T. Yau, & é. Zaslow, Mirror symmetry is T-duality, Nucl. Phys. B479 (1996) 243-259.
33. G. Tian & S.-T. Yau, Complete Kahler manifolds with zero Ricci curvature. I, J. Amer. Math. Soc. 3 (1990) 579-609.
34. G. Tian & S.-T. Yau, Complete Kahler manifolds with zero Ricci curvature. II, Invent. Math. 106 (1991) 27-60.
35. S.-T. Yau, On the Ricci curvature of a compact Kdhler manifold and the complex Monge-Ampère equation. I, Comm. Pure Appl. Math. 31 (1978) 339-411.
36. S.-T. Yau, Survey on partial differential equations in differential geometry, Seminar on Differential Geom., Ann. of Math. Stud., Princeton Univ. Press, 102 (1982) 3-71.