Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero

Andrey Trepalin

Open Mathematics (2014)

  • Volume: 12, Issue: 2, page 229-239
  • ISSN: 2391-5455

Abstract

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Let 𝕜 be a field of characteristic zero and G be a finite group of automorphisms of projective plane over 𝕜 . Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field 𝕜 is algebraically closed. In this paper we prove that ℙ 𝕜 2 ℙ 𝕜 2 G G is rational for an arbitrary field 𝕜 of characteristic zero.

How to cite

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Andrey Trepalin. "Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero." Open Mathematics 12.2 (2014): 229-239. <http://eudml.org/doc/269772>.

@article{AndreyTrepalin2014,
abstract = {Let \[\mathbb \{k\}\] be a field of characteristic zero and G be a finite group of automorphisms of projective plane over \[\mathbb \{k\}\] . Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field \[\mathbb \{k\}\] is algebraically closed. In this paper we prove that \[\{\{\mathbb \{P\}\_\mathbb \{k\}^2 \} \mathord \{\left\bad. \{\vphantom\{\{\mathbb \{P\}\_\mathbb \{k\}^2 \} G\}\} \right. \hspace\{0.0pt\}\} G\}\] is rational for an arbitrary field \[\mathbb \{k\}\] of characteristic zero.},
author = {Andrey Trepalin},
journal = {Open Mathematics},
keywords = {Noether problem; Rationality; del Pezzo surfaces; Minimal Model Program; Cremona group; rationality; minimal model program},
language = {eng},
number = {2},
pages = {229-239},
title = {Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero},
url = {http://eudml.org/doc/269772},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Andrey Trepalin
TI - Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero
JO - Open Mathematics
PY - 2014
VL - 12
IS - 2
SP - 229
EP - 239
AB - Let \[\mathbb {k}\] be a field of characteristic zero and G be a finite group of automorphisms of projective plane over \[\mathbb {k}\] . Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field \[\mathbb {k}\] is algebraically closed. In this paper we prove that \[{{\mathbb {P}_\mathbb {k}^2 } \mathord {\left\bad. {\vphantom{{\mathbb {P}_\mathbb {k}^2 } G}} \right. \hspace{0.0pt}} G}\] is rational for an arbitrary field \[\mathbb {k}\] of characteristic zero.
LA - eng
KW - Noether problem; Rationality; del Pezzo surfaces; Minimal Model Program; Cremona group; rationality; minimal model program
UR - http://eudml.org/doc/269772
ER -

References

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