Geodesic
On birational involutions of~$\mathbb P^3$
Izvestiya. Mathematics , Tome 77 (2013) no. 3, pp. 627-648

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We study elements $\tau$ of order two in the birational automorphism groups of rationally connected three-dimensional algebraic varieties such that there exists a non-uniruled divisorial component of the $\tau$-fixed point locus. Using the equivariant minimal model program, we give a rough classification of such elements.
Keywords: rational map, Cremona group, Fano variety. 
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     author = {Yu. G. Prokhorov},
     title = {On birational involutions of~$\mathbb P^3$},
     journal = {Izvestiya. Mathematics },
     pages = {627--648},
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Yu. G. Prokhorov. On birational involutions of~$\mathbb P^3$. Izvestiya. Mathematics , Tome 77 (2013) no. 3, pp. 627-648. http://geodesic.mathdoc.fr/item/IM2_2013_77_3_a10/