The DOI matches its Crossref record; 32 of the 32 references it cites were found in a registry or an index.
Introduction to the Minimal Model Problem
Abstract
Chapter O. Notation and preliminaries § 0-1.Kleiman's criterion for ampleness § 0-2.Definitions of terminal, canonical and (weak) log-terminal singularities § 0-3.Canonical varieties § 0-4.The minimal model conjecture Chapter 1. Vanishing theorems § 1-1.Covering Lemma § 1-2.Vanishing theorem of Kawamata and Viehweg § 1-3.Vanishing theorem of Elkik and Fujita Chapter 2. Non-Vanishing Theorem § 2-1.Non-Vanishing Theorem Chapter 3. Base Point Free Theorem § 3-1.Base Point Free Theorem § 3-2.Contractions of extremal faces § 3-3.Canonical rings of varieties of general type Chapter 4. Cone Theorem § 4-1.Rationality Theorem § 4-2.The proof of the Cone Theorem Chapter 5. Flip Conjecture § 5-1.Types of contractions of extremal rays § 5-2.Flips of toric morphisms Chapter 6. Abundance Conjecture § 6-1.Nef and abundant divisors
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Citations
Cites
Hartshorne, R. (1966) · Lecture Notes in Mathematics · doi:10.1007/bfb0080482 · Cited by 1,721
Threefolds Whose Canonical Bundles Are Not Numerically Effective
Мори, Ш. (1982) · Annals of Mathematics · doi:10.2307/2007050 · Cited by 620
Projective Manifolds with Ample Tangent Bundles
Мори, Ш. (1979) · Annals of Mathematics · doi:10.2307/1971241 · Cited by 587
Toward a Numerical Theory of Ampleness
Kleiman, S. L. (1966) · Annals of Mathematics · doi:10.2307/1970447 · Cited by 503
Kawamata, Y. (1988) · The Annals of Mathematics · doi:10.2307/1971417 · Cited by 413
Self-citationA generalization of Kodaira-Ramanujam's vanishing theorem
Kawamata, Y. (1982) · Mathematische Annalen · doi:10.1007/bf01456407 · Cited by 356
Self-citationThe Chern Classes and Kodaira Dimension of a Minimal Variety
Miyaoka, Y. (2018) · Advanced studies in pure mathematics · doi:10.2969/aspm/01010449 · Cited by 335
Minimal Models of Canonical 3-Folds
Reid, M. A. (2018) · Advanced studies in pure mathematics · doi:10.2969/aspm/00110131 · Cited by 292
The Theorem of Riemann-Roch for High Multiples of an Effective Divisor on an Algebraic Surface
Zariski, O. (1962) · The Annals of Mathematics · doi:10.2307/1970376 · Cited by 278
Pluricanonical systems on minimal algebraic varieties
Kawamata, Y. (1985) · Inventiones Mathematicae · doi:10.1007/bf01388524 · Cited by 257
Self-citation
Cited by
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
“Kawamata, Matusda and Matsuki proved [22] the termination of terminal 4-fold flips, Matsuki has shown [29] the termination of terminal 4-fold flops and Fujino has shown [8] the termination of canonical 4-fold (log) flips.”
Flip theorem and the existence of minimal models for 3-folds
Mori, S. (1988) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-1988-0924704-x · Cited by 313
On the length of an extremal rational curve
Kawamata, Y. (1991) · Inventiones mathematicae · doi:10.1007/bf01232281 · Cited by 154
Self-citationKollár, J. (1993) · Mathematische Annalen · doi:10.1007/bf01445123 · Cited by 118
Metadata
- Authors
- Kawamata, Y., Matsuda, K., & Matsuki, K.
- Venue
- Advanced Studies in Pure Mathematics
- Publisher
- Mathematical Society of Japan
- Published
- 2018-06-06
- Pages
- 283-360
- ISSN
- 0920-1971 (ISSN-L)
- OpenAlex
- W1985584270
- Cited by
- 957
- References
- 32
- FWCI
- 54.47
- Type
- conference paper
- Language
- en
- Open access
- closed
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