Abundance conjecture
In algebraic geometry, the abundance conjecture is a conjecture in
birational geometry, more precisely in the minimal model program,
stating that for every projective variety with Kawamata log terminal singularities over a field if the canonical bundle is nef, then is semi-ample.
Important cases of the abundance conjecture have been proven by Caucher Birkar.{{Cite journal | doi=10.1007/s10240-012-0039-5|title = Existence of log canonical flips and a special LMMP| journal=Publications Mathématiques de l'IHÉS| volume=115| pages=325–368|year = 2012|last1 = Birkar|first1 = Caucher| arxiv=1104.4981}}
References
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- {{Citation | last1=Kollár | first1=János | author1-link = János Kollár | last2=Mori | first2=Shigefumi | author2-link = Shigefumi Mori | title=Birational geometry of algebraic varieties | publisher=Cambridge University Press | series=Cambridge Tracts in Mathematics | isbn=978-0-521-63277-5 |mr=1658959 | year=1998 | volume=134 | at = Conjecture 3.12, p. 81 | url=https://books.google.com/books?id=YrysxvPbBLwC&pg=PA81 }}
- {{citation
| last = Lehmann | first = Brian
| editor1-first = Izzet | editor1-last = Coskun
| editor2-first = Tommaso | editor2-last = de Fernex
| editor3-first = Angela | editor3-last = Gibney
| contribution = A snapshot of the minimal model program
| contribution-url = https://www2.bc.edu/brian-lehmann/papers/snapshot.pdf
| mr = 3727495
| pages = 1–32
| publisher = American Mathematical Society | location = Providence, RI
| series = Proceedings of Symposia in Pure Mathematics
| title = Surveys on recent developments in algebraic geometry: Papers from the Bootcamp for the 2015 Summer Research Institute on Algebraic Geometry held at the University of Utah, Salt Lake City, UT, July 6–10, 2015
| volume = 95
| year = 2017}}
Category:Unsolved problems in geometry
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