Moduli spaces of polarized irreducible symplectic manifolds are not necessarily connected

Apostolov, Apostol

Annales de l'Institut Fourier, Tome 64 (2014) no. 1, pp. 189-202.

Nous montrons que l’espace de modules des variétés symplectiques irréductibles polarisées de type $K{3}^{\left[n\right]}$, le type de polarisation étant fixé, n’est pas nécessairement connexe. Cela peut être obtenu comme une conséquence de la caractérisation de Markman des opérateurs de transport parallèle polarisé de type $K{3}^{\left[n\right]}$.

We show that the moduli space of polarized irreducible symplectic manifolds of $K{3}^{\left[n\right]}$-type, of fixed polarization type, is not always connected. This can be derived as a consequence of Eyal Markman’s characterization of polarized parallel-transport operators of $K{3}^{\left[n\right]}$-type.

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