Existence of minimal models for varieties of log general type II
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Assuming finite generation in dimension n − 1 , we prove that pl-flips exist in dimension n .
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Let f:X→Z be a pl-flipping contraction for an n-dimensional purely log terminal pair (X,∆). Then the flip f+:X+→Z of f exists.
“Theorem A (Existence of pl-flips).Let f : X -→ Z be a pl-flipping contraction for an n-dimensional purely log terminal pair (X, ∆). Then the flip f + : X + -→ Z of f exists.”
From Existence of minimal models for varieties of log general type (2009) · cites this paper as [8]
Cites
Birational Geometry of Algebraic Varieties
Kollár, J., & Mori, S. (1998) · Cambridge University Press eBooks · doi:10.1017/cbo9780511662560 · Cited by 2,165 · see citing works
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 · cited 3× · see citing works
“7) of [2], we may find a positive integer k, a divisor Φ on S and a prime divisor G (necessarily a component of Θ whose coefficient is irrational) such that (1) 0 ≤ Φ ∈ W , (2) both kΦ/r and k∆/r are Cartier, (3) ‖Φ − Θ‖ < min(δ, η, f /k), where f is the smallest non-zero coefficient of F = 0, and (4) multG Φ > multG…”
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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 · see citing works
“ent of the stable base locus of KX +∆. we prove the existence of pl-flips: Theorem A. Pl-flips exist in dimension n. that is, we prove: Theorem 1.2. Theorem Fn−1 implies Theorem An. With the results of [2], (1.2) completes the proof of (1.1). The main ideas used in this paper have their origins in the work of Shokurov o…”
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- Authors
- Hacon, C., & M^{𝑐}Kernan, J.
- Affiliations
- University of Utah (US)
- ORCID
- Hacon, Christopher
- Venue
- Journal of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 2009-11-13
- Volume
- 23
- Issue
- 2
- Pages
- 469-490
- ISSN
- 0894-0347 (ISSN-L)
- 1088-6834
- OpenAlex
- W4231831651
- Cited by
- 38
- References
- 2
- Citations by year
- 2026: 1 · 2025: 2 · 2023: 3 · 2021: 2 · 2020: 2 · 2019: 1 · 2018: 1 · 2017: 5 · 2016: 1 · 2015: 2 · 2014: 2 · 2013: 2 · 2012: 5
- FWCI
- 5.85
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Journal of the American Mathematical Society (publishedVersion, public-domain)
- arXiv (Cornell University) (submittedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc-sa)
- arXiv (Cornell University) (cc-by)
- Funders
- National Science Foundation (0456363, 0701101)
- 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 › Mathematical Physics › Advanced Algebra and Geometry
- Keywords
- minimal models, finite generation, birational geometry, log canonical singularities, higher-dimensional algebraic geometry
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