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If X is a complex projective variety with klt singularities, then the mixedHodge structures on the first two singular cohomology groups are pure. Wedescribe the pieces of the Hodge decomposition in terms of reflexivedifferential forms. Applications include a Lefschetz (1,1) Theorem and a weakanalogue of the Hodge-Riemann bilinear relations for klt varieties.

Low degree Hodge theory for klt varieties