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Quantum Cohomology of Minuscule Homogeneous Spaces

2008; Birkhäuser; Volume: 13; Issue: 1 Linguagem: Inglês

10.1007/s00031-008-9001-5

1531-586X

Pierre–Emmanuel Chaput, Laurent Manivel, Nicolas Perrin,

Algebraic Geometry and Number Theory

We study the quantum cohomology of (co)minuscule homogeneous varieties under a unified perspective. We show that three points Gromov–Witten invariants can always be interpreted as classical intersection numbers on auxiliary varieties. Our main combinatorial tools are certain quivers, in terms of which we obtain a quantum Chevalley formula and a higher quantum Poincaré duality. In particular, we compute the quantum cohomology of the two exceptional minuscule homogeneous varieties.