Quantum cohomology of flag manifolds

Details Quantum cohomology of flag manifolds Quantum cohomology of flag manifolds

2000-10-09

arxiv.org/abs/math/0010080v1

Mathematics

Algebraic Geometry

28 pages, LaTeX

Scientific paper

The (small) quantum cohomology ring of a flag manifold F encodes enumerative geometry of rational curves on F. We give a proof of the presentation of the ring and of a quantum Giambelli formula, which is more direct and geometric than the previously known proof. Furthermore, this proof gives a relationship between quantum Schubert polynomials and universal Schubert polynomials, which arise in a degeneracy locus formula of Fulton.

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