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Journals / Turkish Journal of Mathematics / 2008 / Cilt: 32 - Sayı: 1

Mirror Principle for Flag Manifolds

Vehbi Emrah PAKSOY
Pages
61–82
Publication Date
2022-11-05
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, this can be used as a valuable testing ground for the theories which associates quantum cohomologies and J functions of non-abelian quotient to abelian quotients via quantization.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, using mirror principle developped by Lian, Liu and Yau [8, 9, 10, 11, 12, 13] we obtained the A and B series for the equivariant tangent bundles over homogenous spaces using Chern polynomial.
📊
Key Findings & Data:This is necessary to obtain related cohomology valued series for given arbitrary vector bundle and multiplicative characteristic class.
💡
Conclusion & Impact:Moreover, this can be used as a valuable testing ground for the theories which associates quantum cohomologies and J functions of non-abelian quotient to abelian quotients via quantization.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Turk. J. Math. · (2008) · 61-82. Full text: pdf Other articles published in the same issue: Turk. J. Math.

Abstract

In this paper, using mirror principle developped by Lian, Liu and Yau [8, 9, 10, 11, 12, 13] we obtained the A and B series for the equivariant tangent bundles over homogenous spaces using Chern polynomial. This is necessary to obtain related cohomology valued series for given arbitrary vector bundle and multiplicative characteristic class. Moreover, this can be used as a valuable testing ground for the theories which associates quantum cohomologies and J functions of non-abelian quotient to abelian quotients via quantization.

Özet

In this paper, using mirror principle developped by Lian, Liu and Yau [8, 9, 10, 11, 12, 13] we obtained the A and B series for the equivariant tangent bundles over homogenous spaces using Chern polynomial. This is necessary to obtain related cohomology valued series for given arbitrary vector bundle and multiplicative characteristic class. Moreover, this can be used as a valuable testing ground for the theories which associates quantum cohomologies and J functions of non-abelian quotient to abelian quotients via quantization.

🔖

Cite This Article

PAKSOY, V. E. (2022). Mirror Principle for Flag Manifolds. Turkish Journal of Mathematics, Cilt: 32 - Sayı: 1, 61–82. https://ajindex.com/articles/608598

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References (13)

  1. Brion, M.: Lectures on geometry of flag varieties, math.AG/0410240. Fulton, W.: Intersection theory, Ser. Mod. Surv. Math. 2, Springer-Verlag, 1977.
  2. Fulton, W.:Young tableaux-with applications to representation theory and geometry, London Math. Soc. Student Texts 35, Cambridge Univ. Press. 1997.
  3. Fulton, W., Pandharipande, R.: Notes on stable maps and quantum cohomology in Alge- braic geometry, Santa Cruz 1995, J.Koll´ar, R.Lazarsfeld and D. Morrison eds, Proc. Symp. Pure Math. vol. 62, part 2, pp. 45-96, Amer. Math. Soc. 1997.
  4. Goresky, M., Kottwitz, R., MacPherson, R.: Equivariant cohomology, Kozsul duality and the localization theorem, Invent. Math 131, 25-83 1998.
  5. Kontsevich, M.: Enumeration of rational curves via torus actions, in the Moduli space of curves ed. by R. Dijkgraaf, C. Faber and G. van der Geer, Prog. Math. 129, Birkh¨a user, 368, 1995.
  6. Li, J., Tian, G.: Virtual moduli cycle and Gromov-Witten invariants of algebraic varieties., J. of Amer. Math. Soc. 11:1, 119-174 (1998).
  7. Lian, B., Liu, K., Yau, S.T.: Mirror Principle I, Asian J. Math 1, 729-763 1997.
  8. Lian, B., Liu, K., Yau, S.T.: Mirror Principle II, Asian J. Math 3, 109-146 1999.
  9. Lian, B., Liu, K., Yau, S.T.: Mirror Principle III, Asian J. Math 3, 771-800 1999.
  10. Lian, B., Liu, K., Yau, S.T.: A survey of mirror principal, math.AG/0010064. Lian, B., Liu, C.H, Liu, K., Yau S.T.: S1Şxed points in Quot schemes and mirror symme- try principle computations, in Vector bundles and representation theory, S.D Cutkosky, D.Edidin, Z. Qin and Q. Zhang, eds., Contemp. Math. 332, pp. 165-194,
  11. Amer. Math. Soc., Liu, K., Liu, C.H, Yau, S.T.: S Şxed points in hyper quot schemes and an exact mirror formula for flag manifolds from the extended mirror principle diagram, math.AG/0401367 v1, 2004.
  12. Monk, D.: The geometry of flag manifolds, Proc. London math. Soc.(3) 9, 253-286 1959.
  13. Tu, L.W.: Characteristic numbers of a homogenous spaces, math.AG/0102013 v3, 2003. Vehbi E. PAKSOY Claremont McKenna College N. College Ave, D 323 Claremont, CA, 91711, USA e-mail: [email protected]