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Uspekhi Mat. Nauk, 1986, Volume 41, Issue 2(248), Pages 43–94 (Mi umn1998)  

This article is cited in 20 scientific papers (total in 21 papers)

Rational varieties: algebra, geometry and arithmetic

Yu. I. Manin, M. A. Tsfasman


Full text: PDF file (3747 kB)
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English version:
Russian Mathematical Surveys, 1986, 41:2, 51–116

Bibliographic databases:

UDC: 512.7
MSC: 14M20, 14H25, 14J26, 14J50, 14Exx, 14M10
Received: 07.03.1985

Citation: Yu. I. Manin, M. A. Tsfasman, “Rational varieties: algebra, geometry and arithmetic”, Uspekhi Mat. Nauk, 41:2(248) (1986), 43–94; Russian Math. Surveys, 41:2 (1986), 51–116

Citation in format AMSBIB
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\by Yu.~I.~Manin, M.~A.~Tsfasman
\paper Rational varieties: algebra, geometry and arithmetic
\jour Uspekhi Mat. Nauk
\yr 1986
\vol 41
\issue 2(248)
\pages 43--94
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\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1986RuMaS..41...51M}
\transl
\jour Russian Math. Surveys
\yr 1986
\vol 41
\issue 2
\pages 51--116
\crossref{https://doi.org/10.1070/RM1986v041n02ABEH003242}
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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. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities”, Math. USSR-Sb., 66:1 (1990), 231–248  mathnet  crossref  mathscinet  zmath  isi
    2. V. A. Iskovskikh, “Factorization of birational maps of rational surfaces from the viewpoint of Mori theory”, Russian Math. Surveys, 51:4 (1996), 585–652  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. V. G. Drinfeld, V. A. Iskovskikh, A. I. Kostrikin, A. N. Tyurin, I. R. Shafarevich, “Yurii Ivanovich Manin (on his 60th birthday)”, Russian Math. Surveys, 52:4 (1997), 863–873  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. Degtyarev, A, “Real rational surfaces are quasi-simple”, Journal fur Die Reine und Angewandte Mathematik, 551 (2002), 87  crossref  mathscinet  zmath  isi  elib
    5. E. Ballico, “Geometry of Cubic and Quartic Hypersurfaces over Finite Fields”, Finite Fields and Their Applications, 8:4 (2002), 554  crossref
    6. V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Hyperelliptic and trigonal Fano threefolds”, Izv. Math., 69:2 (2005), 365–421  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. S. Yu. Rybakov, “Zeta functions of conic bundles and Del Pezzo surfaces of degree 4 over finite fields”, Mosc. Math. J., 5:4 (2005), 919–926  mathnet  mathscinet  zmath
    8. G. Berhuy, Z. Reichstein, “On the notion of canonical dimension for algebraic groups”, Advances in Mathematics, 198:1 (2005), 128  crossref
    9. Kharlamov V., “Overview of topological properties of real algebraic surfaces”, Algebraic Geometry and Geometric Modeling, Mathematics and Visualization, 2006, 103–117  isi
    10. N. F. Zak, “Quasi-triviality of forms of Segre varieties”, Russian Math. Surveys, 62:5 (2007), 1018–1020  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. N. F. Zak, “The Unirationality of Quartics over Nonclosed Fields Revisited”, Math. Notes, 84:1 (2008), 38–44  mathnet  crossref  crossref  mathscinet  isi  elib
    12. Ming-chang Kang, Yuri G. Prokhorov, “Rationality of three-dimensional quotients by monomial actions”, Journal of Algebra, 324:9 (2010), 2166  crossref
    13. Ming-chang Kang, “Retract rational fields”, Journal of Algebra, 2011  crossref
    14. Cecilia Salgado, “On the rank of the fibers of elliptic K3 surfaces”, Bull Braz Math Soc, New Series, 43:1 (2012), 7  crossref
    15. Ming-chang Kang, “Bogomolov multipliers and retract rationality for semidirect products”, Journal of Algebra, 397 (2014), 407  crossref
    16. Akinari Hoshi, Ming-chang Kang, Hidetaka Kitayama, “Quasi-monomial actions and some 4-dimensional rationality problems”, Journal of Algebra, 403 (2014), 363  crossref
    17. Huah Chu, Akinari Hoshi, Shou-Jen Hu, Ming-chang Kang, “Noether's problem for groups of order 243”, Journal of Algebra, 2015  crossref
    18. Akinari Hoshi, “Birational classification of fields of invariants for groups of order 128”, Journal of Algebra, 2015  crossref
    19. Yu. G. Prokhorov, “Ratsionalnye poverkhnosti”, Lekts. kursy NOTs, 24, MIAN, M., 2015, 3–76  mathnet  crossref  elib
    20. Auel A. Bernardara M., “Semiorthogonal Decompositions and Birational Geometry of Del Pezzo Surfaces Over Arbitrary Fields”, Proc. London Math. Soc., 117:1 (2018), 1–64  crossref  isi
    21. S. G. Vlăduţ, D. Yu. Nogin, M. A. Tsfasman, “Varieties over finite fields: quantitative theory”, Russian Math. Surveys, 73:2 (2018), 261–322  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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