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Mat. Sb., 1991, Volume 182, Number 10, Pages 1430–1445 (Mi msb1381)  

This article is cited in 2 scientific papers (total in 2 papers)

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

I. Ya. Kolpakov-Miroshnichenkoa, Yu. G. Prokhorovb

a 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).

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

Bibliographic databases:

UDC: 512.776
MSC: Primary 14E05, 14L35, 14H45; Secondary 14H35
Received: 28.05.1990

Citation: I. Ya. Kolpakov-Miroshnichenko, Yu. G. Prokhorov, “Rationality of fields of invariants of some four-dimensional linear groups, and an equivariant construction related to the Segre cubic”, Mat. Sb., 182:10 (1991), 1430–1445; Math. USSR-Sb., 74:1 (1993), 169–183

Citation in format AMSBIB
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\by I.~Ya.~Kolpakov-Miroshnichenko, Yu.~G.~Prokhorov
\paper Rationality of fields of invariants of some four-dimensional linear groups, and an equivariant construction related to the Segre cubic
\jour Mat. Sb.
\yr 1991
\vol 182
\issue 10
\pages 1430--1445
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\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993SbMat..74..169K}
\transl
\jour Math. USSR-Sb.
\yr 1993
\vol 74
\issue 1
\pages 169--183
\crossref{https://doi.org/10.1070/SM1993v074n01ABEH003342}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Hamza Ahmad, Mowaffaq Hajja, Ming-chang Kang, “Rationality of Some Projective Linear Actions”, Journal of Algebra, 228:2 (2000), 643  crossref
    2. H. Chu, S.-J. Hu, M.-c. Kang, B. E. Kunyavskii, “Noether's Problem and the Unramified Brauer Group for Groups of Order 64”, Internat Math Res Notices, 2009  crossref  mathscinet
  • Математический сборник - 1991 Sbornik: Mathematics (from 1967)
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