Mathematics underlying the F-theory/Heterotic String Duality in eight dimensions

Communications in Mathematical Physics

Volumn 254, Issue 3, 2005, Pages 513-563

  Clingher, Adrian ^a,c   Morgan, John W ^b  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b Columbia University ^*  (United States)

^c STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 13844272762     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1270-9     Document Type: Article

References (35)

1. Ash, A., Mumford, D., Rapopon, M., Tai, Y.: Smooth Compactification of Locally Symmetric Varieties. In: Lie Groups: History, Frontiers and Applications, Vol. IV, Brookline, MA: Math. Sci. Press, 1975
2. Aspinwall, P.S., Morrison, D.R.: String Theory on K3 surfaces. In: Mirror symmetry, II, Providence, RI: Amer. Math. Soc., 1997. pp. 703-716
3. Baily, W.L. Jr., Borel, A.: Compactification of Arithmetic Quotients of Bounded Symmetric Domains. Ann. of Math. (2) 84, 442-528 (1966)
4. Barth, W., Peters, C., Van de Ven, A.: Compact Complex Surfaces. Berlin: Springer-Verlag, 1984
5. Carlson, J.A.: Extensions of Mixed Hodge Structures. In: Journées de Géométrie Algébrique d'Angers, Juillet 1979/Algebraic Geometry, Angers, 1979, Alphen aan den Rijn: Sijthoff & Noordhoff, 1980, pp. 107-127
6. Clingher, A.: Heterotic String Data and Theta Functions. http://arxiv.org/abs/math.DG/0110320, 2001
7. Demazure, M., Pinkham, H.C. (eds.): Séminaire sur les Singularités des Surfaces. Volume 777 of Lecture Notes in Mathematics. Berlin: Springer, 1980
8. Freed, D.S.: Dirac Charge Quantization and Generalized Differential Cohomology. In: Surveys in differential geometry, Surv. Differ. Geom., VII, Somerville, MA: International Press, 2000. pp. 129-194
9. Friedman, R.: Hodge Theory, Degenerations and the Global Torelli Problem. Thesis, Harvard University, 1981
10. Friedman, R.: Global Smoothings of Varieties with Normal Crossings. Ann. of Math. (2) 118(1), 75-114 (1983)
11. Friedman, R.: A New Proof of the Global Torelli Theorem for K3 Surfaces. Ann. of Math. (2) 120(2), 237-269 (1984)
12. Friedman, R.: The Period Map at the Boundary of Moduli. In: Topics in transcendental algebraic geometry (Princeton, N.J., 1981/1982), Princeton, NJ: Princeton Univ. Press, 1984, pp. 183-208
13. Friedman, R., Morgan, J., Witten, E.: Vector Bundles and F theory. Commun. Math. Phys. 187(3), 679-743 (1997)
14. Friedman, R., Morgan, J.W.: Principal Holomorphic Bundles over Elliptic Curves IV: del Pezzo Surfaces, in preparation
15. Friedman, R., Morgan, J.W., Witten, E.: Principal G-bundles over Elliptic Curves. Math. Res. Lett. 5(1-2), 97-118 (1998)
16. Ginsparg, P.: On Toroidal Compactification of Heterotic Superstrings. Phys. Rev. D (3) 35(2), 648-654 (1987)
17. Griffiths, P., Schmid, W.: Recent Developments in Hodge Theory: A Discussion of Techniques and Results. In: Discrete subgroups of Lie groups and applicatons to moduli (Internat. Colloq., Bombay, 1973), Bombay: Oxford Univ. Press, 1975, pp. 31-127
18. Griffiths, P.A.: Periods of Integrals on Algebraic Manifolds: Summary of Main Results and Discussion of Open Problems. Bull. Amer. Math. Soc. 76, 228-296 (1970)
19. Kac, V.G., Peterson, D.H. Infinite-Dimensional Lie Algebras, Theta Functions and Modular Forms. Adv. in Math. 53(2), 125-264 (1984)
20. Kulikov, V.S.: Degenerations of K3 Surfaces and Enriques Surfaces. Izv. Akad. Nauk SSSR Ser. Mat. 41(5), 1008-1042, 1199 (1977)
21. Looijenga, E., Peters, C.: Torelli Theorems for Kähler K3 Surfaces. Compositio Math. 42(2), 145-186 (1980/81)
22. Manin, Yu.I.: Cubic Forms: Algebra, Geometry, Arithmetic. Amsterdam: North-Holland Publishing Co., 1986
23. Mumford, D.: Tata Lectures on Theta. I (with the assistance of C. Musili, M. Nori, E. Previato and M. Stillman), Boston, MA: Birkhäuser Boston Inc., 1983
24. Narain, K.S.: New Heterotic String Theories in Uncompactified Dimensions < 10. Phys. Lett. B 169(1), 41-46 (1986)
25. Narain, K.S., Sarmadi, M.H., Witten, E.: A Note on Toroidal Compactification of Heterotic String Theory. Nucl. Phys. B 279(3-4), 369-379 (1987)
26. Dolgachev, I.V.: Mirror Symmetry for Lattice Polarized K3 Surfaces. J. Math. Sci. 81(3), 2599-2630 (1996)
27. Persson, U., Pinkham, H.: Degeneration of Surfaces with Trivial Canonical Bundle. Ann. of Math. (2) 113(1), 45-66 (1981)
28. Pjateckiǐ-Šapiro, I.I., Šafarevič, I.R.: Torelli's Theorem for Algebraic Surfaces of Type k3. Izv. Akad. Nauk SSSR Ser. Mat. 35, 530-572 (1971)
29. Schmid, W.: Variation of Hodge Structure: The Singularities of the Period Mapping. Invent. Math. 22, 211-319 (1973)
30. Sen, A.: F-Theory and Orientifolds. Nucl. Phys. B 475(3), 562-578 (1996)
31. Cardoso, G., Curio, G., Lust, D., Mohaupt, T.: On the duality between the heterotic string and F-theory in 8 dimensions. Phys. Lett. B 389(3), 479-484 (1996)
32. Siegel, C.L.: Advanced Analytic Number Theory. Second edition, Bombay: Tata Institute of Fundamental Research, 1980
33. Siu, Y.T., Trautmann, G.: Deformations of Coherent Analytic Sheaves with Compact Supports. Mem. Amer. Math. Soc. 29(238). iii+155 (1981)
34. Vafa, C.: Evidence for F-theory. Nucl. Phys. B 469(3), 403-415 (1996)
35. Witten, E.: World-Sheet Corrections via D-instantons. J. High Energy Phys. 2, Paper 30, 18 (2000)