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Mat. Sb., 2016, Volume 207, Number 3, Pages 3–18 (Mi msb8554)  

This article is cited in 3 scientific papers (total in 3 papers)

Automorphisms of threefolds that can be represented as an intersection of two quadrics

A. Avilov

National Research University "Higher School of Economics" (HSE), Moscow

Abstract: We prove that any $G$-del Pezzo threefold of degree $4$, except for a one-parameter family and four distinguished cases, can be equivariantly reconstructed to the projective space $\mathbb P^3$, a quadric $Q\subset\mathbb P^4$, a $G$-conic bundle or a del Pezzo fibration. We also show that one of these four distinguished varieties is birationally rigid with respect to an index $2$ subgroup of its automorphism group.
Bibliography: 15 titles.

Keywords: del Pezzo varieties, automorphism groups, birational rigidity.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-02164
15-01-02158
Ministry of Education and Science of the Russian Federation МК-696.2014.1
This work was partially supported by the Russian Foundation for Basic Research (grants nos. 15-01-02164 and 15-01-02158) and by the Programme of Support of Young Candidates of Sciences of the President of the Russian Federation (grant no. MK-696.2014.1).


DOI: https://doi.org/10.4213/sm8554

Full text: PDF file (519 kB)
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English version:
Sbornik: Mathematics, 2016, 207:3, 315–330

Bibliographic databases:

UDC: 512.765
MSC: 14J50
Received: 07.06.2015

Citation: A. Avilov, “Automorphisms of threefolds that can be represented as an intersection of two quadrics”, Mat. Sb., 207:3 (2016), 3–18; Sb. Math., 207:3 (2016), 315–330

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Avilov, “Automorphisms of Singular Cubic Threefolds and the Cremona Group”, Math. Notes, 100:3 (2016), 482–485  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. Avilov, “Automorphisms of singular three-dimensional cubic hypersurfaces”, Eur. J. Math., 4:3 (2018), 761–777  crossref  mathscinet  zmath  isi  scopus
    3. A. Avilov, “Biregular and birational geometry of quartic double solids with 15 nodes”, Izv. Math., 83:3 (2019), 415–423  mathnet  crossref  crossref  adsnasa  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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