On the Hard Lefschetz property of stringy Hodge numbers

For projective varieties with a certain class of 'mild' isolated singularities and for projective threefolds with arbitrary Gorenstein canonical singularities, we show that the stringy Hodge numbers satisfy the Hard Lefschetz property (i.e. h(st)(p.q) <= h(st)(p+1,q+1) for p + q <= d - 2, where d is the dimension of the variety). This result fits nicely with a 6-dimensional counterexarnple of Mustata and Payne for the Hard Lefschetz property for stringy Hodge numbers in general. We also give Such an example, ours is a hypersurface singularity. (C) 2008 Elsevier Inc. All rights reserved.