On the rationality of certain Fano threefolds

Author:

Ciliberto CiroORCID

Abstract

AbstractIn this paper we study the rationality problem for Fano threefolds $$X\subset {\mathbb P}^{p+1}$$ X P p + 1 of genus p, that are Gorenstein, with at most canonical singularities. The main results are: (1) a trigonal Fano threefold of genus p is rational as soon as $$p\geqslant 8$$ p 8 (this result has already been obtained in Przyjalkowski et al. (Izv Math 69(2):365–421, 2005), but we give here an independent proof); (2) a non-trigonal Fano threefold of genus $$p\geqslant 7$$ p 7 containing a plane is rational; (3) any Fano threefold of genus $$p\geqslant 17$$ p 17 is rational; (4) a Fano threefold of genus $$p\geqslant 12$$ p 12 containing an ordinary line $$\ell $$ in its smooth locus is rational.

Funder

Università degli Studi di Roma Tor Vergata

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

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