Mirror symmetry and toric degenerations of partial flag manifolds

Acta Mathematica

Volumn 184, Issue 1, 2000, Pages 1-39

  Batyrev, Victor V ^a   Kim, Bumsig ^c   Ciocan Fontanine, Ionuţ ^b   Van Straten, Duco ^d  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b NORTHWESTERN UNIVERSITY   (United States)

^c Pohang University of Science and Technology (POSTECH)   (South Korea)

^d JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002176646     PISSN: 00015962     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02392780     Document Type: Article

References (31)

1. n1,...,nk . Comm. Math. Phys., 170 (1995), 503-528.
2. BATYREV, V. V., On classifications of smooth projective toric varieties. Tôhoku Math. J., 43 (1991), 569-585.
3. _ Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties. J. Algebraic Geom., 3 (1994), 493-535.
4. _ Toric degenerations of Fano varieties and constructing mirror manifolds. alg-geom/ 9712034.
5. BATYREV, V. V. & BORISOV, L. A., Dual cones and mirror symmetry for generalized Calabi-Yau manifolds, in Mirror Symmetry, Vol. II, pp. 71-86. AMS/IP Stud. Adv. Math., 1. Amer. Math. Soc., Providence, RI, 1997.
6. BATYREV, V. V., CIOCAN-FONTANINE, I., KIM, B. & STRATEN, D. VAN, Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians. Nuclear Phys. B, 514 (1998), 640-666 (alg-geom/9710022).
7. BATYREV, V. V. & STRATEN, D. VAN, Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties. Comm. Math. Phys., 168 (1995), 493-533 (alg-geom/9307010).
8. BEHREND, K., Gromov-Witten invariants in algebraic geometry. Invent. Math., 127 (1997), 601-617.
9. BORISOV, L. A., Towards mirror symmetry of Calabi-Yau complete intersections in Gorenstein toric Fano varieties. alg-geom/9310001.
10. CANDELAS, P., OSSA, X. DE LA, GREEN, P. & PARKES, L., A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory. Nuclear Phys. B, 359 (1991), 21-74.
11. CIOCAN-FONTANINE, I., On quantum cohomology rings of partial flag varieties. Duke Math. J., 98 (1999), 485-524.
12. EGUCHI, T., HORI, K. & XIONG, C.-S., Gravitational quantum cohomology. Internat. J. Modern Phys. A, 12 (1997), 1743-1782 (hep-th/9605225).
13. EHRESMANN, C., Sur la topologie des certaines espaces homogènes. Ann. of Math., 35 (1934), 396-443.
14. FULTON, W., Introduction to Toric Varieties. Ann. of Math. Stud., 131. Princeton Univ. Press, Princeton, NJ, 1993.
15. GIVENTAL, A., Equivariant Gromov-Witten invariants. Iternat. Math. Res. Notices, 1996, 613-663 (alg-geom/9603021).
16. _ Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture, in Topics in Singularity Theory: V. I. Arnold's 60th Anniversary Collection, pp. 103-115. Amer. Math. Soc. Transl. Ser. 2, 180. Amer. Math. Soc., Providence, RI, 1997 (alg-geom/9612001).
17. _ Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture, in Topics in Singularity Theory: V. I. Arnold's 60th Anniversary Collection, pp. 103-115. Amer. Math. Soc. Transl. Ser. 2, 180. Amer. Math. Soc., Providence, RI, 1997 (alg-geom/9612001).
18. _ A mirror theorem for toric complete intersections, in Topological Field Theory, Primitive Forms and Related Topics (Kyoto, 1996), pp. 141-175. Progr. Math., 160. Birkhäuser Boston, Boston, MA, 1998 (alg-geom/9701016).
19. _ A mirror theorem for toric complete intersections, in Topological Field Theory, Primitive Forms and Related Topics (Kyoto, 1996), pp. 141-175. Progr. Math., 160. Birkhäuser Boston, Boston, MA, 1998 (alg-geom/9701016).
20. GONCIULEA, N. & LAKSHMIBAI, V., Degenerations of flag and Schubert varieties to toric varieties. Transform. Groups, 1 (1996), 215-248.
21. _ Schubert varieties, toric varieties, and ladder determinantal varieties. Ann. Inst. Fourier (Grenoble), 47 (1997), 1013-1064.
22. KIM, B., Quantum cohomology of partial flag manifolds and a residue formula for their intersection pairings. Internat. Math. Res. Notices, 1995, 1-16.
23. _ On equivariant quantum cohomology. Internat. Math. Res. Notices, 1996, 841-851.
24. Quantum cohomology of flag manifolds G/B and quantum Toda lattices. Ann. of Math., 149 (1999), 129-148.
25. _ Quantum hyperplane section theorem for homogeneous spaces. Acta Math., 183 (1999), 71-99 (alg-geom/9712008).
26. LAKSHMIBAI, V., Degenerations of flag varieties to toric varieties. C. R. Acad. Sci. Paris Sér. I Math., 321 (1995), 1229-1234.
27. LI, J. & TIAN, G., Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties. J. Amer. Math. Soc., 11 (1998), 119-174.
28. REID, M., Decomposition of toric morphisms, in Arithmetic and Geometry, Vol. II, pp. 395-418. Progr. Math., 36. Birkhäuser Boston, Boston, MA, 1983.
29. REID, M., Decomposition of toric morphisms, in Arithmetic and Geometry, Vol. II, pp. 395-418. Progr. Math., 36. Birkhäuser Boston, Boston, MA, 1983.
30. SCHECHTMAN, V., On hypergeometric functions connected with quantum cohomology of flag spaces. q-alg/9712049.
31. STURMFELS, B., Gröbner Bases and Convex Polytopes. Univ. Lecture Ser., 8. Amer. Math. Soc., Providence, RI, 1996.