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Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 3, Pages 199–222 (Mi izv8014)  

This article is cited in 4 scientific papers (total in 4 papers)

On birational involutions of $\mathbb P^3$

Yu. G. Prokhorovab

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b National Research University "Higher School of Economics"

Abstract: We study elements $\tau$ of order two in the birational automorphism groups of rationally connected three-dimensional algebraic varieties such that there exists a non-uniruled divisorial component of the $\tau$-fixed point locus. Using the equivariant minimal model program, we give a rough classification of such elements.

Keywords: rational map, Cremona group, Fano variety.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00336-a
11-01-92613-KO_a
Ministry of Education and Science of the Russian Federation НШ-4713.2010.1
11.G34.31.0023
Simons Foundation


DOI: https://doi.org/10.4213/im8014

Full text: PDF file (655 kB)
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English version:
Izvestiya: Mathematics, 2013, 77:3, 627–648

Bibliographic databases:

Document Type: Article
UDC: 512.76
MSC: 14E07, 20B25
Received: 22.06.2012
Revised: 30.11.2012

Citation: Yu. G. Prokhorov, “On birational involutions of $\mathbb P^3$”, Izv. RAN. Ser. Mat., 77:3 (2013), 199–222; Izv. Math., 77:3 (2013), 627–648

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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. A. A. Avilov, “Existence of standard models of conic fibrations over non-algebraically-closed fields”, Sb. Math., 205:12 (2014), 1683–1695  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. J. Déserti, “Some properties of the group of birational maps generated by the automorphisms of $\mathbb{P}_{\mathbb{C}}^{n}$ and th”, Mathematische Zeitschrift, 281 (2015), 893–905  crossref  mathscinet  zmath  elib  scopus
    3. Yu. G. Prokhorov, “Singular Fano threefolds of genus 12”, Sb. Math., 207:7 (2016), 983–1009  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Yuri Prokhorov, Constantin Shramov, “Jordan constant for Cremona group of rank $3$”, Mosc. Math. J., 17:3 (2017), 457–509  mathnet  mathscinet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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