Quantum cohomology of partial flag manifolds and a residue formula for their intersection pairings. (English) Zbl 0849.14019

Under the assumption that the equivariant quantum cohomology of a Kähler manifold is well defined, associative, and a weighted-homogeneous ordinary equivariant \(q\)-deformation of ordinary cohomology, the author computes the equivariant quantum cohomology of partial flag manifolds. The author also derives a general result for some manifolds which present their quantum cohomology as regular functions on complete intersections.


14M15 Grassmannians, Schubert varieties, flag manifolds
57R91 Equivariant algebraic topology of manifolds
81T99 Quantum field theory; related classical field theories
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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