On Verlinde sheaves and strange duality over elliptic Noether-Lefschetz divisors

Marian, Alina; Oprea, Dragos

Annales de l'Institut Fourier, Tome 64 (2014) no. 5, pp. 2067-2086.

On établit l’isomorphisme de dualité étrange pour toutes les surfaces $K3$ constituant un diviseur de Noether-Lefschetz dans l’espace de modules de surfaces $K3$ quasipolarisées. On interprète le résultat d’une manière globale, comme un isomorphisme de faisceaux à travers ce diviseur, et on décrit aussi la construction globale sur l’espace de modules des surfaces $K3s$ polarisées.

We extend results on generic strange duality for $K3$ surfaces by showing that the proposed isomorphism holds over an entire Noether-Lefschetz divisor in the moduli space of quasipolarized $K3$s. We interpret the statement globally as an isomorphism of sheaves over this divisor, and also describe the global construction over the space of polarized $K3s$.

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