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Special cubic birational transformations of projective spaces

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Abstract

We extend our classification of special Cremona transformations whose base locus has dimension at most three to the case when the target space is replaced by a (locally) factorial complete intersection.

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Notes

  1. Notice that the difference between the right and left side of the inequality (2.25) coincides with the sum \(\Sigma _{l}\left( {\begin{array}{c}5+l^2\\ 4\end{array}}\right) \), where l runs over all lines contained in the surface \(S\subset {{\mathbb {P}}}^5\) having self-intersection \(\le -2\). Thus (2.25) is a strict inequality if and only if S contains a line with self-intersection \(\le -6\).

  2. For further computational details, see the online documentation of the methods abstractRationalMap from Cremona [72], and dualVariety from Resultants [73].

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Acknowledgements

The author is grateful to Francesco Russo for useful discussions and for his interest in the work.

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    Giovanni Staglianò

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Staglianò, G. Special cubic birational transformations of projective spaces. Collect. Math. 71, 123–150 (2020). https://doi.org/10.1007/s13348-019-00251-8

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