Speaker
Nao Moriyama
(Kyoto U.)
Description
$\mathbb{Q}$-factoriality or log canonicity}
The minimal model program (MMP) and the abundance conjecture are central
problems in birational geometry. The MMP for log surfaces holds under
standard assumptions, such as $\mathbb{Q}$-factoriality or log canonicity.
In this talk, we show that the MMP for log surfaces fails in general. On
the other hand, intriguingly, we also mention that the abundance theorem
still holds for log surfaces in such a setting where the MMP fails. This
talk is based on the author's preprint (arXiv:2602.00732) and joint work
with Makoto Enokizono (arXiv:2609.12478).