Abstract
We construct a deformation family for each of the 34 Hilbert series of Fano 3-folds in codimension 4 having Fano index 2. In 18 cases we construct two different families, distinguished by the topology of their general members.
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Notes
The Hilbert series with ID # 40367 and # 40378 also appear in the GRDB in index 2 and codimension 4. However, the Fano 3-folds associated to these two Hilbert series cannot embed in codimension 4 in the weighted projective space suggested by the Graded Ring Database. These two Fano 3-folds may exist embedded in higher codimension. They also do not have a candidate double cover X in codimension 4 having Fano index 1. Indeed, neither our method nor the method in [10] construct them.
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Acknowledgements
The author would like to thank Gavin Brown, Tiago Guerreiro, Stavros Argyrios Papadakis, Kaori Suzuki, and Miles Reid for conversations and comments during the development of this work.
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Campo, L. Fano 3-folds and double covers by half elephants. European Journal of Mathematics 9, 98 (2023). https://doi.org/10.1007/s40879-023-00689-y
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DOI: https://doi.org/10.1007/s40879-023-00689-y