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Singularities of Toric Manifolds

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By using methods of toric geometry, we investigate compactifications of F-theory on the elliptic Calabi–Yau threefolds.

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REFERENCES

  1. M. Bershadsky, K. Intriligator, S. Kachru, D. Morrison, V. Sadov, and C. Vafa, “Geometric singularities and enhanced gauge symmetries,” Nucl. Phys. B, 481, 215–252 (1996).

    Google Scholar 

  2. P. Candelas and A. Font, “Duality between the webs of heterotic and type II vacua,” Nucl. Phys. B, 511, 295–325 (1998).

    Google Scholar 

  3. P. Candelas, E. Perevalov, and G. Rajesh, “Toric geometry and enhanced gauge symmetry of F-theory / heterotic vacua,” Nucl. Phys. B, 507, 445–474 (1997).

    Google Scholar 

  4. E. Perevalov and H. Skarke, “Enhanced gauge symmetry in type II and F-theory compactifications. Dynkin diagrams from polyhedra,” Nucl. Phys. B, 505, 679–700 (1997).

    Google Scholar 

  5. P. Candelas, E. Perevalov, and G. Rajesh, “Matter from toric geometry,” Nucl. Phys. B, 519, 225–238 (1998).

    Google Scholar 

  6. W. Fulton, Introduction to Toric Varieties, Princeton University Press, Princeton (1993).

    Google Scholar 

  7. R. Rajaraman, Solitons and Instantons, North-Holland, Amsterdam (1982).

    Google Scholar 

  8. D. R. Morrison and C. Vafa, “Compactifications of F-theory on Calabi-Yau threefolds. I,” Nucl. Phys. B, 473, 74–92 (1996).

    Google Scholar 

  9. D. R. Morrison and C. Vafa, “Compactifications of F-theory on Calabi-Yau threefolds. II,” Nucl. Phys. B, 476, 437–469 (1996).

    Google Scholar 

  10. S. Hosono, A. Klemm, S. Theisen, and S.-T. Yau, “Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces,” Commun. Math. Phys., 167, 301–350 (1995).

    Google Scholar 

  11. S. Hosono, A. Klemm, S. Theisen, and S.-T. Yau, “Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces,” Nucl. Phys. B, 433, 501–554 (1995).

    Google Scholar 

  12. T. Christo and A. Loebel, PORTA — A Polyhedron Representation Transformation Algorithm, The Electronic Library for Mathematical Software (http://elib.zib.de).

  13. K. Kodaira, “On compact analytic surface: II,” Ann. Math., 77, 563–626 (1963).

    Google Scholar 

  14. J. Tate, “Algorithm for determining the type of a singular fiber in an elliptic pencil, in modular functions of one variable,” in: Lect. Notes Math. Ser., 476, Springer, Berlin (1975).

    Google Scholar 

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Authors and Affiliations

  1. Institute for Nuclear Research, Ukrainian Academy of Sciences, Kiev

    T. V. Obikhod

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  1. T. V. Obikhod
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Obikhod, T.V. Singularities of Toric Manifolds. Ukrainian Mathematical Journal 53, 299–305 (2001). https://doi.org/10.1023/A:1010429423301

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