Reider-type inequalities imply nefness of dH-E on blow-ups of P^3 along surfaces and sharp ample cone estimates for Hilbert schemes of length-d subschemes via Bridgeland semistability chambers and the Bayer-Macri theorem.
Fano visitor problem for K3 surfaces
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Two New Extensions of Reider's Theorem on Algebraic Surfaces
Reider-type inequalities imply nefness of dH-E on blow-ups of P^3 along surfaces and sharp ample cone estimates for Hilbert schemes of length-d subschemes via Bridgeland semistability chambers and the Bayer-Macri theorem.