The DOI matches its Crossref record; 46 of the 46 references it cites were found in a registry or an index.
Flips for 3-folds and 4-folds
Abstract
The minimal model program in algebraic geometry is a conjectural sequence of algebraic surgery operations that simplifies any algebraic variety to a point where it can be decomposed into pieces with negative, zero, and positive curvature, in a similar vein as the geometrization program in topology decomposes a three-manifold into pieces with a standard geometry. The last few years have seen dramatic advances in the minimal model program for higher dimensional algebraic varieties, with the proof of the existence of minimal models under appropriate conditions, and the prospect within a few years ... More
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“Theorem F n-1 implies Theorem A n ; see the main result of [9].”
From Existence of minimal models for varieties of log general type (2009) · cites this paper as [9]
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“Proof of Theorems A, B, C, D, E and F. This is immediate from the main result of [9] and Lemmas 4.4, 5.6, 6.6, 7.3 and 8.1.”
From Existence of minimal models for varieties of log general type (2009) · cites this paper as [9]
Citations
Cites
Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I
Hironaka, H. (1964) · Annals of Mathematics · doi:10.2307/1970486 · Cited by 2,256
Positivity in Algebraic Geometry I
Lazarsfeld, R. (2004) · Springer eBooks · doi:10.1007/978-3-642-18808-4 · Cited by 1,576
Variation of hodge structure: The singularities of the period mapping
Schmid, W. (1973) · Inventiones Mathematicae · doi:10.1007/bf01389674 · Cited by 817
Higher-Dimensional Algebraic Geometry
Debarre, O. (2001) · Universitext · doi:10.1007/978-1-4757-5406-3 · Cited by 732
Kodaira, K. (2015) · Princeton University Press eBooks · doi:10.1515/9781400869879-002 · Cited by 724
Algebraic approximation of structures over complete local rings
Artin, M. (1969) · Publications mathématiques de l IHÉS · doi:10.1007/bf02684596 · Cited by 697
Higher Direct Images of Dualizing Sheaves I
Kollár, J. (1986) · Annals of Mathematics · doi:10.2307/1971351 · Cited by 548
Families of rationally connected varieties
Graber, T., Harris, J., & Starr, J. (2002) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-02-00402-2 · Cited by 476
Kawamata, Y. (1988) · Annals of Mathematics · doi:10.2307/1971417 · Cited by 463
Steenbrink, J. H. M. (1976) · Inventiones mathematicae · doi:10.1007/bf01403146 · Cited by 370
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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
Singular Kähler-Einstein metrics
Eyssidieux, P., Guedj, V., & Zeriahi, A. (2009) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-09-00629-8 · Cited by 305
Metadata
- Venue
- Oxford University Press eBooks
- Publisher
- Oxford University Press
- Published
- 2007-06-01
- OpenAlex
- W1534491398
- Cited by
- 56
- References
- 46
- Citations by year
- 2025: 1 · 2024: 3 · 2023: 4 · 2022: 2 · 2021: 3 · 2020: 3 · 2018: 1 · 2017: 3 · 2016: 5 · 2015: 2 · 2014: 2 · 2013: 3 · 2012: 9
- FWCI
- 2.31
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Oxford University Press eBooks (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 › Algebra and Number Theory › Advanced Algebra and Geometry
- Keywords
- c-FLIP, minimal model program, algebraic varieties, 3-folds, minimal models, higher-dimensional algebraic geometry, positive curvature, negative curvature
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