Compactifications of moduli spaces inspired by mirror symmetry
Journées de géométrie algébrique d'Orsay - Juillet 1992, Astérisque, no. 218 (1993), p. 243-271
     author = {Morrison, David R.},
     title = {Compactifications of moduli spaces inspired by mirror symmetry},
     booktitle = {Journ\'ees de g\'eom\'etrie alg\'ebrique d'Orsay - Juillet 1992},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {218},
     year = {1993},
     pages = {243-271},
     language = {en},
     url = {}
Morrison, David R. Compactifications of moduli spaces inspired by mirror symmetry, in Journées de géométrie algébrique d'Orsay - Juillet 1992, Astérisque, no. 218 (1993), pp. 243-271.

1. A. Ash, D. Mumford, M. Rapoport, and Y. Tai, Smooth compactifications of locally symmetric varieties, Lie Groups : History, Frontiers and Applications, vol. IV, Math Sci Press, Brookline (Mass.), 1975.

2. P. S. Aspinwall, B. R. Greene, and D. R. Morrison, Multiple mirror manifolds and topology change in string theory, Phys. Lett. B, 303 (1993), 249-259.

3. P. S. Aspinwall and C. A. Lütken, Quantum algebraic geometry of superstring compactifications, Nuclear Phys. B 355 (1991), 482-510.

4. P. S. Aspinwall and D. R. Morrison, Topological field theory and rational curves, Comm. Math. Phys. 151 (1993), 245-262.

5. W. L. Baily, Jr. and A. Borel, Compactification of arithmetic quotients of bounded symmetric domains, Annals of Math. (2) 84 (1966), 442-528.

6. V. V. Batyrev, Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori, Duke. Math. J. 69 (1993), 349-409.

7. A. Beauville, Variétés Kählereinnes dont la première classe de Chern est nulle, J. Diff. Geom. 18 (1983), 755-782.

8. F. A. Bogomolov, Hamiltonian Kähler manifolds, Dokl. Akad. Nauk SSSR 243 (1978), no. 5, 1101-1104.

9. C. Borcea, On desingularized Horrocks-Mumford quintics, J. Reine Angew. Math. 421 (1991), 23-41.

10. A. Borel, Some metric properties of arithmetic quotients of symmetric spaces and an extension theorem, J. Diff. Geom. 6 (1972), 543-560.

11. 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.

12. 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), 21-74.

13. P. Candelas, M. Lynker, and R. Schimmrigk, Calabi- Yau manifolds in weighted P4, Nuclear Phys. B 341 (1990), 383-402.

14.E. Cattani and A. Kaplan, Polarized mixed Hodge structures and the local monodromy of a variation of Hodge structure, Invent. Math. 67 (1982), 101-115.

15. S. Cecotti, N=2 Landau-Ginzburg vs. Calabi-Yau σ-models : Non-perturbative aspects, Internat. J. Modern Phys. A 6 (1991), 1749-1813.

16. P. Deligne, Equations différentielles à points singuliers réguliers, Lecture Notes in Math., vol. 163, Springer-Verlag, Berlin, Heidelberg, New York, 1970.

17. P. Deligne, La conjecture de Weil, II, Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137-252.

18. L. J. Dixon, Some world-sheet properties of superstring compactifications, on orbifolds and otherwise, Superstrings, Unified Theories, and Cosmology 1987 (G. Furlan et al., eds.), World Scientific, Singapore, New Jersey, Hong Kong, 1988, pp. 67-126.

19. W. Fulton, Introduction to toric varieties, Annals of Math. Studies, vol. 131, Princeton University Press, Princeton, 1993.

20. G. Van Der Geer, Hilbert modular surfaces, Ergeb. Math. Grenzgeb. (3) 16, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1988.

21. A. Grassi and D. R. Morrison, Automorphisms and the Kahler cone of certain Calabi-Yau manifolds, Duke Math. J. 71 (1993), 831-838.

22. M. B. Green, J. H. Schwarz, and E. Witten, Superstring theory, Cambridge University Press, Cambridge, 1987.

23. B. R. Greene, D. R. Morrison, and M. R. Plesser, Mirror manifolds in higher dimension, preprint, 1993.

24. B. R. Greene and M. R. Plesser, Duality in Calabi-Yau moduli space, Nuclear Phys. B 338 (1990), 15-37.

25. P. A. Griffiths, Periods of integrals on algebraic manifolds: Summary of main results and discussion of open problems, Bull. Amer. Math. Soc. 76 (1970), 228-296.

26. P. A. Griffiths, ed., Topics in transcendental algebraic geometry, Annals of Math. Studies, vol. 106, Princeton University Press, Princeton, 1984.

27. J. C. Hemperly, The parabolic contribution to the number of linearly independent automorphic forms on a certain bounded domain, Amer. J. Math. 94 (1972), 1078-1100.

28. F. E. P. Hirzebruch, Hilbert modular surfaces, Enseign. Math. (2) 19 (1973), 183-282.

29. T. Hübsch, Calabi-Yau manifolds : A bestiary for physicists, World Scientific, Singapore, New Jersey, London, Hong Kong, 1992.

30. J. Igusa, A desingularization problem in the theory of Siegel modular functions, Math. Ann. 168 (1967), 228-260.

31. Y. Kawamata, Crepent blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces, Annals of Math. (2) 127 (1988), 93-163.

32. A. Landman, On the Picard-Lefschetz transformations, Trans. Amer. Math. Soc. 181 (1973), 89-126.

33. H. B. Laufer, Taut two-dimensional singularities, Math. Ann. 205 (1973), 131-164.

34. W. Lerche, C. Vafa, and N. P. Warner, Chiral rings in N=2 superconformal theories, Nuclear Phys. B 324 (1989), 427-474.

35. E. Looijenga, New compactifications of locally symmetric varieties, Proceedings of the 1984 Vancouver Conference in Algebraic Geometry (J. Carrell et al., eds.), CMS Conference Proceedings, vol. 6, American Mathematical Society, Providence, 1986, pp. 341-364.

36. S. Mori, Threefolds whose canonical bundles are not numerically effective, Annals of Math. (2) 116 (1982), 133-176.

37. S. Mori, Hartshorne conjecture and extremal ray, Sugaku Expositions 1 (1988), 15-37.

38. D. R. Morrison, The Kuga-Satake variety of an abelian surface, J. Algebra 92 (1985), 454-476.

39. D. R. Morrison, Picard-Fuchs equations and mirror maps for hypersurfaces, Essays on Mirror Manifolds (S.-T. Yau, ed.), International Press Co., Hong Kong, 1992, pp. 241-264.

40. D. R. Morrison, Mirror symmetry and rational curves on quintic threefolds : A guide for mathematicians, J. Amer. Math. Soc. 6 (1993), 223-247.

41. D. R. Morrison, Hodge-theoretic aspects of mirror symmetry, in preparation.

42. D. Mumford, The topology of normal singularities of an algebraic surface and a criterion for simplicity, Inst. Hautes Études Sci. Publ. Math. 9 (1961), 5-22.

43. T. Oda, Convex bodies and algebraic geometry: An introduction to the theory of toric varieties, Ergeb. Math. Grenzgeb. (3) 15, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1988.

44. K. Oguiso, On algebraic fiber space structures on a Calabi-Yau 3-fold, Int. J. Math. 4 (1993), 439-465.

45. R. T. Rockafellar, Convex analysis, Princeton University Press, Princeton, 1970.

46. I. Satake, On the compactification of the Siegel space, J. Indian Math. Soc. (N.S.) 20 (1956), 259-281.

47. I. Satake, On the arithmetic of tube domains (blowing-up of the point at infinity), Bull. Amer. Math. Soc. 79 (1973), 1076-1094.

48. W. Schmid, Variation of Hodge structure: The singularities of the period mapping, Invent. Math. 22 (1973), 211-319.

49. C. Schoen, On fiber products of rational elliptic surfaces with section, Math. Z. 197 (1988), 177-199.

50. H. J. M. Sterk, Compactifications of the period space of Enriques surfaces: Arithmetic and geometric aspects, Ph.D. thesis, Katholiecke Universiteit Nijmegen, 1988.

51. G. Tian, Smoothness of the universal deformation space of compact Calabi-Yau manifolds and its Peterson-Weil metric, Mathematical Aspects of String Theory (S.-T. Yau, ed.), World Scientific, Singapore, 1987, pp. 629-646.

52. A. N. Todorov, The Weil-Peters son geometry of the moduli space of SU(n3) (Calabi-Yau) manifolds, I, Comm. Math. Phys. 126 (1989), 325-246.

53. E. Viehweg, Weak positivity and the stability of certain Hilbert points. III, Invent. Math. 101 (1990), 521-543.

54. P. Wagreich, Singularities of complex surfaces with solvable local fundamental group, Topology 11 (1972), 51-72.

55. P. M. H. Wilson, The Kähler cone on Calabi-Yau threefolds, Invent. Math. 107 (1992), 561-583.

56. E. Witten, Topological sigma models, Comm. Math. Phys. 118 (1988), 411-449.

57. E. Witten, On the structure of the topological phase of two-dimensional gravity, Nuclear Phys. B 340 (1990), 281-332.

58. E. Witten, Mirror manifolds and topological field theory, Essays on Mirror Manifolds (S.-T. Yau, ed.), International Press Co., Hong Kong, 1992, pp. 120-159.

59. E. Witten, Phases of N=2 theories in two dimensions, Nuclear Phys. B 403 (1993), 159-222.

60. S.-T. Yau, On Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), 1798-1799.