Title: Log Hodge groups on a toric Calabi-Yau degeneration Authors: Helge Ruddat Categories: math.AG math.CV Comments: 48 pages, 3 figures MSC-class: 14J32; 32S35; 14M25 \ We give a spectral sequence to compute the logarithmic Hodge groups on a hypersurface type toric log Calabi-Yau space, compute its E_1 term explicitly in terms of tropical degeneration data and Jacobian rings and prove its degeneration at E_2 under mild assumptions. We prove the basechange of the affine Hodge groups and deduce it for the logarithmic Hodge groups in low dimensions. As an application, we prove a mirror symmetry duality in dimension two and four involving the usual Hodge numbers, the stringy Hodge numbers and the affine Hodge numbers. \ ( http://arxiv.org/abs/0906.4809 , 58kb)
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