The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
3-Fold log models
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In the citing paper
“(1) There are finitely many birational contractions φ i : X Y i over U , 1 ≤ i ≤ p such that E A,π (V ) = p i=1 W i , where each W i = W φ i ,A,π (V ) is a rational polytope.Moreover, if φ : X Y is a log terminal model of (X, ∆) over U , for some ∆ ∈ E A,π (V ), then φ = φ i , for some 1 ≤ i ≤ p.”
From Existence of minimal models for varieties of log general type (2009) · cites this paper as [32]
Citations
Cites
Kawamata, Y. (1988) · Annals of Mathematics · doi:10.2307/1971417 · Cited by 463
Flips and Abundance for Algebraic Threefolds
Kollár, J. (1992) · Astérisque · Cited by 439
Young person’s guide to canonical singularities
Reid, M. A. (1987) · Proceedings of symposia in pure mathematics · doi:10.1090/pspum/046.1/927963 · Cited by 406
Shokurov, V. V. (1993) · Izvestiya Mathematics · doi:10.1070/im1993v040n01abeh001862 · Cited by 229
Self-citationClassification of three-dimensional flips
Kollár, J., & Мори, Ш. (1992) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-1992-1149195-9 · Cited by 170
On the length of an extremal rational curve
Kawamata, Y. (1991) · Inventiones mathematicae · doi:10.1007/bf01232281 · Cited by 154
Abundance theorem for minimal threefolds
Kawamata, Y. (1992) · Inventiones mathematicae · doi:10.1007/bf02100604 · Cited by 143
Zariski, O. (1958) · Cited by 121
Log abundance theorem for threefolds
Keel, S., Matsuki, K., & McKernan, J. (1994) · Duke Mathematical Journal · doi:10.1215/s0012-7094-94-07504-2 · Cited by 113
Two two-dimensional terminations
Alexeev, V. A. (1993) · Duke Mathematical Journal · doi:10.1215/s0012-7094-93-06922-0 · Cited by 70
Minimal discrepancies of toric singularities
Borisov, A. (1997) · manuscripta mathematica · doi:10.1007/bf02678179 · Cited by 41
TERMINATION OF LOG FLIPS FOR ALGEBRAIC 3-FOLDS
Kawamata, Y. (1992) · International Journal of Mathematics · doi:10.1142/s0129167x92000308 · Cited by 41
Abundance conjecture for 3-folds : case $\nu = 1$
Miyaoka, Y. (1988) · French digital mathematics library (Numdam) · Cited by 29
The Cone Theorem: Note to a Paper of Y. Kawamata, 119 (1984), 603-633
Kollár, J. (1984) · Annals of Mathematics · doi:10.2307/2007069 · Cited by 15
Nikulin, V. V. (2012) · Higher Dimensional Complex Varieties · doi:10.1515/9783110814736.261 · Cited by 5
Flagged first, then by citations
Research works printed but not linked: 13
- J. W. S. Cassels,An Introduction to Diophantine Approximations, Cambridge University Press (1957).
- A. Corti,Factoring Birational Maps of Threefolds After Sarkisov, preprint.
- Y. Kawamata, “The minimal discrepancy coefficients of terminal singularities of dimension 3”, Appendix to [26],Izv. Akad. Nauk SSSR. Ser. Mat.,56, No. 1, 201–203 (1992).
- Y. Kawamata, K. Matsuda, and K. Matsuki, “Minimal model problem”, In:Adv. Stud. Pure Math., Vol. 10, Kinokuniya Company (1987), pp. 283–360.
- T. Luo,On the Divisorial Extremal Contractions of Threefolds: Divisor to a Point, preprint.
- M. Reid, “Minimal models of canonical threefolds”, In:Algebraic Varieties and Analytic Varieties, Adv. Stud. Pure Math., Vol. 1, Kinokuniya and North Holland (1983), pp. 131–180.
- M. Reid,Birational Geometry of 3-Folds According to Sarkisov, preprint (1991).
- V. G. Sarkisov,Birational Maps of Standard ℚ-Fano Fiberings, I. V. Kurchatov Institute Atomic Energy preprint (1989).
- V. V. Shokurov, “A nonvanishing theorem”,Izv. Akad. Nauk SSSR. Ser. Mat.,49, 635–651 (1985).
- V. V. Shokurov, “Problems about Fano varieties”, In:Birational Geometry of Algebraic Varieties: Open problems. The XXIIIrd International Symposium, Division of Mathematics, The Taniguchi Foundation. Aug. 22–27, 1988, pp. 30–32.
- V. V. Shokurov,Special 3-Dimensional Flips, preprint, MPI/89-22.
- V. V. Shokurov, “Semi-stable 3-fold flips”,Izv. Akad. Nauk SSSR. Ser. Mat.,57, No. 2, 162–224 (1993).
- V. V. Shokurov,A.c.c. of m.l.d., preprint.
Cited by
Sorted by citations
Existence of minimal models for varieties of log general type
Birkar, C., Cascini, P., Hacon, C., & McKernan, J. (2009) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-09-00649-3 · Cited by 1,278
(2007) · doi:10.1093/acprof:oso/9780198570615.001.0001 · Cited by 56
Metadata
- Authors
- Shokurov, V. V.
- Venue
- Journal of Mathematical Sciences
- Published
- 1996-09
- Volume
- 81
- Issue
- 3
- Pages
- 2667-2699
- ISSN
- 1072-3374 (ISSN-L)
- 1573-8795
- OpenAlex
- W1968474946
- Cited by
- 135
- References
- 15
- Citations by year
- 2026: 2 · 2025: 4 · 2024: 3 · 2023: 3 · 2022: 3 · 2021: 9 · 2020: 8 · 2019: 8 · 2018: 4 · 2017: 2 · 2016: 3 · 2015: 2 · 2014: 4 · 2013: 5 · 2012: 6
- FWCI
- 2.89
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Journal of Mathematical Sciences (publishedVersion)
- Funders
- National Science Foundation (9200933)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic Geometry and Number Theory
- Physical Sciences › Mathematics › Geometry and Topology › Geometry and complex manifolds
- Physical Sciences › Mathematics › Algebra and Number Theory › Commutative Algebra and Its Applications
- Keywords
- log minimal model program, 3-folds, log canonical singularities, Q-divisors, contraction theorem
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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