V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities”, Math. USSR-Sb., 66:1 (1990), 231

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Mathematics of the USSR-Sbornik, 1990, Volume 66, Issue 1, Pages 231–248
DOI: https://doi.org/10.1070/SM1990v066n01ABEH001314 (Mi sm1607)

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

Del Pezzo surfaces with log-terminal singularities

V. V. Nikulin

English version PDF (1002 kB) Citations (18) Russian version article

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DOI: https://doi.org/10.1070/SM1990v066n01ABEH001314

Abstract: A new method is applied to the study of del Pezzo surfaces

Z

$Z$ with log-terminal singularities, taken from the theory of reflection groups in Lobachevsky space. This method yields bounds on the Picard number

ρ (Y)

$\rho(Y)$ of a minimal resolution

Y

$Y$ of singularities of

Z

$Z$ , assuming that the indices or the multiplicities of the singularities of

Z

$Z$ are bounded, and under an extra (conjecturally inessential) condition of generality on the singularities of

Z

$Z$ .
Bibliography: 25 titles.

Received: 12.01.1988

Bibliographic databases:

Document Type: Article

UDC: 512.744

MSC: Primary 14J26; Secondary 14J05, 14J17, 14J25, 14E30, 51F15, 05C99

Language: English

Original paper language: Russian

Citation: V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities”, Math. USSR-Sb., 66:1 (1990), 231–248

Citation in format AMSBIB

\Bibitem{Nik89}

\by V.~V.~Nikulin

\paper Del Pezzo surfaces with log-terminal singularities

\jour Math. USSR-Sb.

\yr 1990

\vol 66

\issue 1

\pages 231--248

\mathnet{http://mi.mathnet.ru/eng/sm1607}

\crossref{https://doi.org/10.1070/SM1990v066n01ABEH001314}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=993456}

\zmath{https://zbmath.org/?q=an:0704.14030|0674.14024}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1990DK06800013}

Linking options:

https://www.mathnet.ru/eng/sm1607

https://doi.org/10.1070/SM1990v066n01ABEH001314

https://www.mathnet.ru/eng/sm/v180/i2/p226

Cycle of papers

Del Pezzo surfaces with log-terminal singularities
V. V. Nikulin
Mat. Sb., 1989, 180:2, 226–243
Del Pezzo surfaces with log-terminal singularities. II
V. V. Nikulin
Izv. Akad. Nauk SSSR Ser. Mat., 1988, 52:5, 1032–1050
Del Pezzo surfaces with log-terminal singularities. III
V. V. Nikulin
Izv. Akad. Nauk SSSR Ser. Mat., 1989, 53:6, 1316–1334

This publication is cited in the following 18 articles:

José Cogolludo-Agustín, Tamás László, Jorge Martín-Morales, András Némethi, Contemporary Mathematics, 778, 𝑝-Adic Analysis, Arithmetic and Singularities, 2022, 231
Dimitrios I. Dais, “Toric log del Pezzo surfaces with one singularity”, Advances in Geometry, 20:1 (2020), 121
Hideo Kojima, Takeshi Takahashi, “Normal del Pezzo surfaces of rank one with log canonical singularities”, Journal of Algebra, 360 (2012), 53
G. D. Noce, “On the Picard Number of Singular Fano Varieties”, International Mathematics Research Notices, 2012
Kasprzyk A.M., Kreuzer M., Nill B., “On the Combinatorial Classification of Toric Log Del Pezzo Surfaces”, LMS J. Comput. Math., 13 (2010), 33–46
Dais D.I., “Classification of Toric Log Del Pezzo Surfaces Having Picard Number 1 and Index <= 3”, Results Math., 54:3-4 (2009), 219–252
Okada T., “On the Birational Unboundedness of Higher Dimensional Q-Fano Varieties”, Math. Ann., 345:1 (2009), 195–212
Lin, JY, “Birational unboundedness of Q-Fano threefolds”, International Mathematics Research Notices, 2003, no. 6, 301
Yu. G. Prokhorov, V. V. Shokurov, “The first main theorem on complements: from global to local”, Izv. Math., 65:6 (2001), 1169–1196
D.-Q. ZHANG, “Quotients of K3 surfaces modulo involutions”, Jpn. j. math, 24:2 (1998), 335
Nikulin V., “Basis of the Diagram Method for Generalized Reflection Groups in Lobachevsky Spaces and Algebraic Surfaces with Nef Anticanonical Class”, Int. J. Math., 7:1 (1996), 71–108
R. Blache, “Riemann-Roch theorem for normal surfaces and applications”, Abh Math Semin Univ Hambg, 65:1 (1995), 307
R. Blache, “Two aspects of log terminal surface singularities”, Abh Math Semin Univ Hambg, 64:1 (1994), 59
Nikulin V., “On the Picard Number of Fano 3-Folds with Terminal Singularities”, J. Math. Kyoto Univ., 34:3 (1994), 495–529
V. V. Nikulin, “Algebraic three-folds and the diagram method”, Math. USSR-Izv., 37:1 (1991), 157–189
V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. III”, Math. USSR-Izv., 35:3 (1990), 657–675
V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. II”, Math. USSR-Izv., 33:2 (1989), 355–372
V. A. Alexeev, “Fractional indices of log Del Pezzo surfaces”, Math. USSR-Izv., 33:3 (1989), 613–629

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

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Abstract page:	589
Russian version PDF:	143
English version PDF:	29
References:	67
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