The termination of flips conjecture asserts that a sequence of flips for a log canonical pair cannot be infinite.
The ordinary adjoint is 
, and the generalized-pair version uses 
with one fixed nef b-divisor
throughout. In the NQC formulation, this b-divisor
is determined on a birational model by a finite nonnegative real linear combination
of nef rational Cartier divisors (Chen and Tsakanikas 2023). Termination of every
permitted sequence is stronger than existence of one finite minimal model program.
Termination of Flips Conjecture
See also
b-Divisor, Flip, Generalized Pair, Kaehler Manifold, Log Canonical Pair, Minimal Model Program, Mori Fiber SpaceExplore with Wolfram|Alpha
References
Birkar, C. "Lectures on Birational Geometry." 9 Oct 2012. https://arxiv.org/abs/1210.2670.Chen, G. and Tsakanikas, N. "On the Termination of Flips for Log Canonical Generalized Pairs." Acta Math. Sin. Engl. Ser. 39, 967-994, 2023. https://doi.org/10.1007/s10114-023-0116-3.Cite this as:
Weisstein, Eric W. "Termination of Flips Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TerminationofFlipsConjecture.html