A. A. Zagorskii, “Three-dimensional conical fibrations”, Mat. Zametki, 21:6 (1977), 745–758; Math. Notes, 21:6 (1977), 420

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Matematicheskie Zametki, 1977, Volume 21, Issue 6, Pages 745–758 (Mi mzm8005)

This article is cited in 11 scientific papers (total in 11 papers)

Three-dimensional conical fibrations

A. A. Zagorskii

Moscow Textile Institute

Full-text PDF (1011 kB) Citations (11)

Abstract: The investigation of conical fibrations initiated by M. Artin and D. Mumford, and by A. N. Tyurin (for the case of a nonsingular degeneracy divisor) is extended to the general case. The main results are: a canonical birational model is found for varieties of a given type; the cohomology groups are computed for the canonical models.

Received: 27.05.1975

English version:
Mathematical Notes, 1977, Volume 21, Issue 6, Pages 420–427
DOI: https://doi.org/10.1007/BF01410168

Bibliographic databases:

UDC: 513

Language: Russian

Citation: A. A. Zagorskii, “Three-dimensional conical fibrations”, Mat. Zametki, 21:6 (1977), 745–758; Math. Notes, 21:6 (1977), 420–427

Citation in format AMSBIB

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\paper Three-dimensional conical fibrations

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\yr 1977

\vol 21

\issue 6

\pages 745--758

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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=463181}

\zmath{https://zbmath.org/?q=an:0399.14026|0369.14008}

\transl

\jour Math. Notes

\yr 1977

\vol 21

\issue 6

\pages 420--427

\crossref{https://doi.org/10.1007/BF01410168}

Linking options:

https://www.mathnet.ru/eng/mzm8005

https://www.mathnet.ru/eng/mzm/v21/i6/p745

This publication is cited in the following 11 articles:

Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456
Ivan Cheltsov, Victor Przyjalkowski, Constantin Shramov, “Quartic double solids with icosahedral symmetry”, Eur. J. Math., 2:1 (2016), 96–119
A. A. Avilov, “Existence of standard models of conic fibrations over non-algebraically-closed fields”, Sb. Math., 205:12 (2014), 1683–1695
A. Iliev, L. Katzarkov, V. Przyjalkowski, “Double solids, categories and non-rationality”, Proc. Edinburgh Math. Soc. (2), 57:1 (2014), 145–173
M. M. Grinenko, “Fibrations into del Pezzo surfaces”, Russian Math. Surveys, 61:2 (2006), 255–300
I. A. Cheltsov, “Conic bundles with big discriminant loci”, Izv. Math., 68:2 (2004), 429–434
B. Crauder, “Degenerations of minimal ruled surfaces”, Ark. Mat., 28:1-2 (1990), 259
S. Yu. Èndryushka, “The intermediate Jacobian of a three-dimensional conic bundle is a Prym variety”, Math. USSR-Sb., 50:1 (1985), 269–277
V. G. Sarkisov, “On conic bundle structures”, Math. USSR-Izv., 20:2 (1983), 355–390
V. G. Sarkisov, “Birational automorphisms of conic bundles”, Math. USSR-Izv., 17:1 (1981), 177–202
V. G. Sarkisov, “Birational automorphisms of 3-dimensional algebraic varieties representable in the form of a conic bundle”, Russian Math. Surveys, 34:4 (1979), 183–184

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

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