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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Quantum cohomology of projective bundles over $\mathbb P^n$
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by Zhenbo Qin and Yongbin Ruan PDF
Trans. Amer. Math. Soc. 350 (1998), 3615-3638 Request permission


In this paper we study the quantum cohomology ring of certain projective bundles over the complex projective space $\mathbb {P}^{n}$. Using excessive intersection theory, we compute the leading coefficients in the relations among the generators of the quantum cohomology ring structure. In particular, Batyrev’s conjectural formula for quantum cohomology of projective bundles associated to direct sum of line bundles over $\mathbb {P}^{n}$ is partially verified. Moreover, relations between the quantum cohomology ring structure and Mori’s theory of extremal rays are observed. The results could shed some light on the quantum cohomology for general projective bundles.
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Additional Information
  • Zhenbo Qin
  • Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
  • Email:
  • Yongbin Ruan
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • Email:
  • Received by editor(s): September 1, 1996
  • Additional Notes: Both authors were partially supported by NSF grants. The second author also had a Sloan fellowship.
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 3615-3638
  • MSC (1991): Primary 58D99, 14J60; Secondary 14F05, 14J45
  • DOI:
  • MathSciNet review: 1422617