Nef cycles on some hyperkahler fourfolds
classification
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keywords
cyclesfourfoldssurfacesconescubicexamplesfailhilbert
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We study the cones of surfaces on varieties of lines on cubic fourfolds and Hilbert schemes of points on K3 surfaces. From this we obtain new examples of nef cycles which fail to be pseudoeffective.
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Twisted cotangent bundles of Hyperk\"ahler manifolds
Lower bound in terms of q(H) for Ω_X ⊗ H to be pseudoeffective on hyperkähler X with ample H; explicit version and optimality check when X deforms to a K3 Hilbert scheme.
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