The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
On the length of an extremal rational curve
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In the citing paper
“If R is an extremal ray of NE(X/U ) that is (K X + ∆)-negative, then there is a rational curve Σ spanning R, such that 0 < -(K X + ∆) • Σ ≤ 2n.”
From Existence of minimal models for varieties of log general type (2009) · cites this paper as [16]
Citations
Cites
Introduction to the Minimal Model Problem
Kawamata, Y., Matsuda, K., & Matsuki, K. (2018) · Advanced studies in pure mathematics · doi:10.2969/aspm/01010283 · Cited by 1,039
Self-citationThreefolds Whose Canonical Bundles Are Not Numerically Effective
Мори, Ш. (1982) · Annals of Mathematics · doi:10.2307/2007050 · Cited by 619
The Cone of Curves of Algebraic Varieties
Kawamata, Y. (1984) · Annals of Mathematics · doi:10.2307/2007087 · Cited by 256
Self-citationA Numerical Criterion for Uniruledness
Miyaoka, Y., & Мори, Ш. (1986) · Annals of Mathematics · doi:10.2307/1971387 · Cited by 216
Generalized adjunction and applications
Ionescu, P. (1986) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100064409 · Cited by 165
The Lower Semi-Continuity of the Plurigenera of Complex Varieties
Nakayama, N. (2018) · Advanced studies in pure mathematics · doi:10.2969/aspm/01010551 · Cited by 50
Moderate degenerations of algebraic surfaces
Kawamata, Y. (1992) · Lecture notes in mathematics · doi:10.1007/bfb0094514 · Cited by 24
Self-citationThe 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
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
Shokurov, V. V. (1996) · Journal of Mathematical Sciences · doi:10.1007/bf02362335 · Cited by 135
Metadata
- Authors
- Kawamata, Y.
- Venue
- Inventiones mathematicae
- Published
- 1991-12
- Volume
- 105
- Issue
- 1
- Pages
- 609-611
- ISSN
- 0020-9910 (ISSN-L)
- 1432-1297
- OpenAlex
- W1981413258
- Cited by
- 154
- References
- 8
- Citations by year
- 2026: 3 · 2025: 4 · 2024: 5 · 2023: 6 · 2022: 4 · 2021: 9 · 2020: 7 · 2019: 7 · 2018: 10 · 2017: 7 · 2016: 5 · 2015: 10 · 2014: 7 · 2013: 4 · 2012: 5
- FWCI
- 1.97
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Inventiones mathematicae (publishedVersion)
- 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 › Applied Mathematics › Geometric Analysis and Curvature Flows
- Keywords
- rational curves, arc length, algebraic geometry, algebraic surfaces
About these checks
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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