218 research outputs found
Log Hodge groups on a toric Calabi-Yau degeneration
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.Comment: 49 pages, 3 figure
Local Gromov-Witten Invariants are Log Invariants
We prove a simple equivalence between the virtual count of rational curves in
the total space of an anti-nef line bundle and the virtual count of rational
curves maximally tangent to a smooth section of the dual line bundle. We
conjecture a generalization to direct sums of line bundles.Comment: 15 pages, version accepted for publication in Advances in Mathematic
Motivic Zeta Functions of the Quartic and its Mirror Dual
We use a formula of Bultot to compute the motivic zeta function for the toric degeneration of the quartic K3 and its Gross-Siebert mirror dual degeneration. We check for this explicit example that the identification of the logarithm of the monodromy and the mirror dual Lefschetz operator works at an integral level
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