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Hyperelliptic and trigonal Fano threefolds

Ivan Cheltsov·Constantin Shramov·Victor Przyjalkowski
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Abstract

We classify Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system has no base points but does not give an embedding, and we classify anticanonically embedded Fano 3-folds with canonical Gorenstein singularities which are not intersections of quadrics. We also study the rationality questions for most of these varieties.

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Ivan Cheltsov, Constantin Shramov, Victor Przyjalkowski. 2005-06-13. Hyperelliptic and trigonal Fano threefolds. https://arxiv.org/abs/math/0406143

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