Refined strange duality under big-and-nef theta line bundles

Establish whether, for primitive positive Mukai vectors on a polarized K3 surface satisfying the Marian–Oprea strange-duality hypotheses, the strange duality map is necessarily zero or an isomorphism when both associated theta line bundles are big and nef, in particular when both are ample.

Background

The paper constructs three counterexamples to the Marian–Oprea strange duality conjecture as originally stated. In each example, at least one theta line bundle is non-nef, has negative degree on an effective divisor of square −2, and exhibits excess vanishing of the sections arising from the strange duality map.

The authors propose imposing positivity on both theta line bundles. Under the big-and-nef assumption, Kawamata–Viehweg vanishing gives equality between Euler characteristics and dimensions of spaces of sections, so the remaining issue is whether the determinant section induces a map of full rank. The paper reports no counterexample to this refined formulation.