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

Alina Marian;  Dragos Oprea — 2014

Annales de l’institut Fourier

We extend results on generic strange duality for K 3 surfaces by showing that the proposed isomorphism holds over an entire Noether-Lefschetz divisor in the moduli space of quasipolarized K 3 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 K 3 s .

On the strange duality conjecture for abelian surfaces

Alina Marian;  Dragos Oprea — 2014

Journal of the European Mathematical Society

We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of equal ranks and ber degree 1. The birational type of the moduli space of sheaves is also investigated. Generalizations to arbitrary product elliptic surfaces are given.

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