On the quantum cohomology of Fano bundles over projective spaces

2000/12/07 by Vincenzo Ancona, Ancona, Vincenzo, Marco Maggesi +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0012046

5 pages, plain TeX. The mistaken identity (4), together with some statements, has been corrected

arxiv created 2000/12/16 · arxiv updated 2009/11/30

Abstract

In their paper "Quantum cohomology of projective bundles over Pⁿ" (Trans. Am. Math. Soc. (1998)350:9 3615-3638) Z.Qin and Y.Ruan introduce interesting techniques for the computation of the quantum ring of manifolds which are projectivized bundles over projective spaces; in particular, in the case of splitting bundles they prove under some restrictions the formula of Batyrev about the quantum ring of toric manifolds. Here we prove the formula of Batyrev on the quantum Chern-Leray equation for a large class of splitting bundles.

Related

• Quantum cohomology of projective bundles over \Peeⁿ
• A Reconstruction Theorem for Quantum Cohomology of Fano Bundles on Projective Space
• Quantum cohomology of projective bundles over Pⁿ
• Quantum Cohomology Rings of Toric Manifolds
• Mirror symmetry and quantum cohomology of projective bundles