Victor V. Przyjalkowski, Constantin A. Shramov, “Double quadrics with large automorphism groups”, Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Trudy Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 167–190; Proc. Steklov Inst. Math., 294 (2016), 154

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 294, Pages 167–190
DOI: https://doi.org/10.1134/S0371968516030109 (Mi tm3739)

This article is cited in 18 scientific papers (total in 18 papers)

Double quadrics with large automorphism groups

Victor V. Przyjalkowski, Constantin A. Shramov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Full-text PDF (308 kB) Citations (18)

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DOI: https://doi.org/10.1134/S0371968516030109

Abstract: We classify nodal Fano threefolds that are double covers of smooth quadrics branched over intersections with quartics and are acted on by finite simple non-abelian groups. We also study their rationality.

Funding agency	Grant number
Russian Science Foundation	14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.

Received: April 1, 2016

English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 294, Pages 154–175
DOI: https://doi.org/10.1134/S0081543816060109

Bibliographic databases:

Document Type: Article

UDC: 512.76

Language: Russian

Citation: Victor V. Przyjalkowski, Constantin A. Shramov, “Double quadrics with large automorphism groups”, Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Trudy Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 167–190; Proc. Steklov Inst. Math., 294 (2016), 154–175

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Linking options:

https://www.mathnet.ru/eng/tm3739

https://doi.org/10.1134/S0371968516030109

https://www.mathnet.ru/eng/tm/v294/p167

This publication is cited in the following 18 articles:

Yuri Prokhorov, “Embeddings of the symmetric groups to the space Cremona group”, Springer Proc. Math. Statist., 409 (2023), 749–762
Alexandra Kuznetsova, “Non-rational sextic double solids”, Math. Z., 301:4 (2022), 4015
I. Cheltsov, J. Park, Yu. Prokhorov, M. Zaidenberg, “Cylinders in Fano varieties”, EMS Surv. Math. Sci., 8:1-2 (2021), 39–105
V. Przyjalkowski, C. Shramov, “Bounds for smooth fano weighted complete intersections”, Commun. Number Theory Phys., 14:3 (2020), 511–553
I. Cheltsov, A. Kuznetsov, C. Shramov, “Coble fourfold, s-6-invariant quartic threefolds, and wiman-edge sextics”, Algebr. Number Theory, 14:1 (2020), 213–274
I. Cheltsov, V. Przyjalkowski, C. Shramov, “Burkhardt quartic, barth sextic, and the icosahedron”, Int. Math. Res. Notices, 2019:12 (2019), 3683–3703
Ivan Cheltsov, Victor Przyjalkowski, Constantin Shramov, “Which quartic double solids are rational?”, J. Algebraic Geom., 28:2 (2019), 201–243
A. G. Kuznetsov, Yu. G. Prokhorov, C. A. Shramov, “Hilbert schemes of lines and conics and automorphism groups of Fano threefolds”, Jap. J. Math., 13:1 (2018), 109–185
Yu. G. Prokhorov, C. A. Shramov, “ $p$ -subgroups in the space Cremona group”, Math. Nachr., 291:8-9 (2018), 1374–1389
Yu. G. Prokhorov, C. A. Shramov, “Finite groups of birational selfmaps of threefolds”, Math. Res. Lett., 25:3 (2018), 957–972
Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456
V. L. Popov, “Compressible finite groups of birational automorphisms”, Dokl. Math., 98:2 (2018), 413–415
V. L. Popov, “The Jordan Property for Lie Groups and Automorphism Groups of Complex Spaces”, Math. Notes, 103:5 (2018), 811–819
Yu. G. Prokhorov, “On the Number of Singular Points of Terminal Factorial Fano Threefolds”, Math. Notes, 101:6 (2017), 1068–1073
Vik. S. Kulikov, E. I. Shustin, “On $G$ -Rigid Surfaces”, Proc. Steklov Inst. Math., 298 (2017), 133–151
Yuri Prokhorov, Constantin Shramov, “Jordan constant for Cremona group of rank $3$ ”, Mosc. Math. J., 17:3 (2017), 457–509
Yu. G. Prokhorov, “A simple proof of the non-rationality of ageneral quartic double solid”, Bull. Korean. Math. Soc., 54:5 (2017), 1619–1625
Yuri G. Prokhorov, “ $\mathbb Q$ -Fano threefolds of index $7$ ”, Proc. Steklov Inst. Math., 294 (2016), 139–153

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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