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Quantum Cohomology of Grassmannians

Published online by Cambridge University Press:  04 December 2007

Anders Skovsted Buch
Anders Skovsted Buch
Affiliation:
Matematish Institut, Aarhus Universitet, Ny Munkegade, 8000 Århus C, Denmark. e-mail: abuch@imf.au.dk
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Abstract

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We give elementary proofs of the main theorems about the (small) quantum cohomology of Grassmannians, including the quantum Giambelli and quantum Pieri formulas, the rim-hook algorithm, the presentation, and a recent theorem of Fulton and Woodward about the minimal q-power which appears in a product of two Schubert classes.

Keywords

quantum cohomologyGromov–Witten invariantsGrassmann varieties
Type
Research Article
Information
Compositio Mathematica , Volume 137 , Issue 2 , June 2003 , pp. 227 - 235
Copyright
© 2003 Kluwer Academic Publishers