I need a reference for an explicit proof of the rationality of the Fano 3-fold $X_{18}$. By explicit I mean by a sequence of explicit birational transformations.
Thank you!
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$\begingroup$ Have you looked into Iskovskikh classification paper? I think he uses the double projection from a line to relate this threefold to something simpler. $\endgroup$– SashaCommented Mar 9, 2016 at 11:02
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$\begingroup$ @Sasha: thank you, which is exactly the paper that you mention? $\endgroup$– IMeasyCommented Mar 9, 2016 at 14:06
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$\begingroup$ it makes sense to start with this springer.com/us/book/9783540614685 book, you will find there a reference (and probably also a construction). $\endgroup$– SashaCommented Mar 9, 2016 at 17:04
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