\(G\)-Fano threefolds. I. (Q2844283)

The paper under review studies \(G\)-Fano 3-folds over a field \(k\) of characteristic zero. These are Fano 3-folds admitting an action of a finite group \(G\), where \(G\) is either the Galois group of the algebraic closure of \(k\), or a group acting on the automorphisms of \(X\). For \(G\)-varieties it is possible to develop a \(G\)-Minimal Model Program. With this the author is able to classify terminal \(G\)-del Pezzo 3-folds under the assumption that the \(G\) invariant part of the Weil divisor class group is of rank 1. The output is a quite compact list of 3-folds, many of those admitting lots of symmetries. The result could be useful to study finite subgroups of the Cremona group of \(\mathbb P^3\). For Part II see [\textit{Y. Prokhorov}, Adv. Geom. 13, No. 3, 419--434 (2013; Zbl 1291.14025)]