Families of quintic Calabi-Yau 3-folds with discrete symmetries

Communications in Mathematical Physics

Volumn 280, Issue 3, 2008, Pages 675-725

  Doran, Charles ^a   Greene, Brian ^b,c   Judes, Simon ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b Columbia University ^*  (United States)

^c Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 43149095323     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-008-0473-x     Document Type: Article

References (34)

1. Witten E. (1985). Symmetry Breaking Patterns In Superstring Models. Nucl. Phys. B 258: 75
2. Greene, B.R., Kirklin, K.H., Miron, P.J., Ross, G.G.: A Three Generation Superstring Model. 1. Compactification And Discrete Symmetries. Nucl. Phys. B 278, 667 (1986) low energy theory.
3. Greene, B.R., Kirklin, K.H., Miron, P.J., Ross, G.G.: A Three Generation Superstring Model. 2. Symmetry Breaking And The Nucl. Phys. B 292, 606 (1987)
4. Braun, V., He, Y.H., Ovrut, B.A., Pantev, T.: A heterotic standard model. Phys. Lett. B 618, 252 (2005).
5. Braun, V., Ovrut, B.A., Pantev, T., Reinbacher, R.: Elliptic Calabi-Yau threefolds with Z(3) x Z(3) Wilson lines. JHEP 0412, 062 (2004)
6. Candelas P. (1988). Yukawa Couplings Between (2,1) Forms. Nucl. Phys. B 298: 458
7. 3 Yukawa Couplings For A Three Generation Superstring Model. Phys. Lett. B 192: 111
8. Giryavets A., Kachru S., Tripathy P.K. and Trivedi S.P. (2004). Flux compactifications on Calabi-Yau threefolds. JHEP 0404: 003
9. Gukov S., Vafa C. and Witten E. (2000). CFT's from Calabi-Yau four-folds. Nucl. Phys. B 584: 69 [Erratum-ibid. B 608, 477 (2001)]
10. Giddings S.B., Kachru S. and Polchinski J. (2002). Hierarchies from fluxes in string compactifications. Phys. Rev. D 66: 106006 [arXiv:hep-th/ 0105097]
11. Candelas, P., de la Ossa, X., Rodriguez-Villegas, F.: Calabi-Yau manifolds over finite fields. I. http://arXiv.org/list/hep-th/0012233,2000
12. Greene B.R. and Plesser M.R. (1990). Duality In Calabi-Yau Moduli Space. Nucl. Phys. B 338: 15
13. Green, M.B., Schwarz, J.H., Witten, E.: Superstring Theory. Vol. 2: Loop Amplitudes, Anomalies And Phenomenology. Cambridge: Camb. Univ. Press. 1987
14. Candelas P., DeLa Ossa X.C., Green P.S. and Parkes L. (1991). A Pair Of Calabi-Yau Manifolds As An Exactly Soluble Superconformal Theory. Nucl. Phys. B 359: 21
15. Headrick M. and Wiseman T. (2005). Numerical Ricci-flat metrics on K3. Class. Quant. Orav. 22: 4931-4960
16. Greene, B.R., Plesser, M.R., Roan, S.S.: In: 'Mirror Symmetry I', New constructions of mirror manifolds: Probing moduli space far from Fermat points, Somerville, MA: International Press, 1998
17. Szendröi B. (2004). On an example of Aspinwall and Morrison. Proc. Amer. Math. Soc. 132(3): 621-632
18. Griffiths P.A. (1969). On the Periods of Certain Rational Integrals. Ann. of Math. (2) 90: 460-495
19. Griffiths, P.A. (Ed.): Topics in transcendental algebraic geometry Annals of Mathematics Studies, 106. Princeton, NJ: Princeton University Press, 1984
20. Cox, D.A., Katz, S.: Mirror Symmetry and Algebraic Geometry. Providence, RI: Amer. Math. Sec., 1999
21. Greene, B.R., Plesser, M.R.: Mirror manifolds: A Brief review and progress report. http://arXiv:hep-th/9110014
22. Dwork B. (1964). On The Zeta function of a hypersurface. II. Ann. of Math. (2) 80: 227-299
23. Carlson J., Müller-Stach S. and Peters C. (2003). Period Mappings and Period Domains. Cambridge University Press, Cambridge
24. Ohara K. (1997). Computation of the Monodromy of the Generalized Hypergeometric Function. Kyushu J. Math. 51: 101-124
25. Morrison, D.: Mathematical aspects of mirror symmetry Complex. In: Algebraic Geometry, J. Kollár, ed., IAS/Park City Math. Series, Vol. 3, 1997, pp. 265-340
26. Doran, C.F., Morgan, J.W.: Mirror symmetry and integral variations of Hodge structure underlying one parameter families of Calabi-Yau threefolds. In: Mirror Symmetry v., AMS/IP Vol. 38, Providence, RI: Amer. Math. Sec., 2006
27. Hosono S., Klemm A., Theisen S. and Yau S.-T. (1995). Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces. Commun. Math. Phys. 167: 301-350
28. Coates, T., Corti, A., Iritani, H., Tseng, H.: Wall-Crossings in Toric Gromov-Witten Theory I: Crepant Examples. http://arxiv.org/list/math.AG/0611550, 2006
29. Doran, C.F., Greene, B.R., Judes, S., Whitcher, U.: In preparation
30. Nikulin V.V. (1979). Finite groups of automorphisms of Kählerian K3 surfaces. (Russian) Trudy Moskov. Mat. Obshch. 38: 75-137
31. Oguiso, K.: Automorphism groups in a family of K3 surfaces. http://arxiv.org/list/0104049, 2001
32. Dolgachev, I.: Weighted projective varieties. In: Group Actions and Vector Fields, J. B. Carell, ed., Lecture Notes in Math., Vol. 956, Springer-Verlag, Berlin, Heidelberg, New York: 1982, pp. 34-37;
33. J. Steenbrink, Intersection form for quasi-homogeneous singularities. Comp. Math. 34 (1977), 211-223.
34. D. Morrison, Picard-Fuchs equations and mirror maps for hypersurfaces. http://arxiv.org/list/9111025, 1991