This article is cited in 4 papers

Rationality of fields of invariants of some four-dimensional linear groups, and an equivariant construction related to the Segre cubic

I. Ya. Kolpakov-Miroshnichenko^a, Yu. G. Prokhorov<sup>b

a</sup> M. V. Lomonosov Moscow State University
^b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Let $G\subset SL(4)$ be a finite primitive linear group. We prove that if $G$ contains a normal subgroup of order 32 then the quotient variety $\mathbf P^3/G$ is birationally isomorphic to $X/G$, where $X$ is the Segre cubic. We also prove the rationality of $\mathbf P^3/G$ for a large class of such groups (in particular, solvable groups).

UDC: 512.776

MSC: Primary 14E05, 14L35, 14H45; Secondary 14H35

Received: 28.05.1990

 English version: Mathematics of the USSR-Sbornik, 1993, 74:1, 169–183

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