Abstract
Let X be a Fano manifold of dimension n and index n − 3. Kawamata proved the non vanishing of the global sections of the fundamental divisor in the case n = 4. Moreover he proved that if Y is a general element of the fundamental system then Y has at most canonical singularities. We prove a generalization of this result in arbitrary dimension.
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Floris, E. Fundamental divisors on Fano varieties of index n − 3. Geom Dedicata 162, 1–7 (2013). https://doi.org/10.1007/s10711-012-9713-5
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DOI: https://doi.org/10.1007/s10711-012-9713-5