Cohomologie quantique des grassmanniennes symplectiques impaires

Abstract : Odd symplectic Grassmannians are a family of quasi-homogeneous spaces that are closely related to symplectic Grassmannians by their construction and properties. The goal of this work is to study their classical and quantum cohomology. For odd symplectic Grassmannians of lines, I obtain a quantum Pieri rule and a presentation of the quantum cohomology ring. I prove the semisimplicity of this ring and determine a full exceptional collection for the derived category, which enables me to check a conjecture of Dubrovin in this example. In the general case, I prove a quantum-to-classical principle for some degree one Gromov-Witten invariants. Assuming higher-dimensional Gromov-Witten invariants are enumerative, I conclude that the quantum Pieri rule is entirely determined by the knowledge of degree one invariants.
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Clélia Pech. Cohomologie quantique des grassmanniennes symplectiques impaires. Mathématiques générales [math.GM]. Université de Grenoble, 2011. Français. ⟨NNT : 2011GRENM059⟩. ⟨tel-00650211⟩

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