• Source: 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



X


{\displaystyle X}

with Kawamata log terminal singularities over a field



k


{\displaystyle k}

if the canonical bundle




K

X




{\displaystyle K_{X}}

is nef, then




K

X




{\displaystyle K_{X}}

is semi-ample.
Important cases of the abundance conjecture have been proven by Caucher Birkar.




References



Kollár, János; Mori, Shigefumi (1998), Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, vol. 134, Cambridge University Press, Conjecture 3.12, p. 81, ISBN 978-0-521-63277-5, MR 1658959
Lehmann, Brian (2017), "A snapshot of the minimal model program" (PDF), in Coskun, Izzet; de Fernex, Tommaso; Gibney, Angela (eds.), 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, Proceedings of Symposia in Pure Mathematics, vol. 95, Providence, RI: American Mathematical Society, pp. 1–32, MR 3727495

Kata Kunci Pencarian:

• Jim Peebles
• Abundance conjecture
• Kodaira dimension
• List of unsolved problems in mathematics
• Minimal model program
• Legendre's conjecture
• Birational geometry
• Yau's conjecture
• Caucher Birkar
• Nef line bundle
• Yujiro Kawamata