On generalized minimal log discrepancy (Q6549920)

Generalized pair is a concept introduced by Birkar which generalizes the concept of a usual pair in birational geometry.\N\NThis paper studies the ACC conjecture and LSC conjecture for minimal log discrepancies of generalized pairs and shows that known results for usual pairs holds also for generalized pairs. The main results are the following:\N\begin{itemize}\N\item[1.] ACC for MLD of generalized pairs holds in dimension \(2\);\N\item[2.] ACC for MLD of generalized pairs with bounded Cartier indices holds;\N\item[3.] ACC for MLD of generalized pairs with canonical singularities in dimension \(3\) holds;\N\item[4.] LSC for MLD of usual pairs implies LSC for MLD of generalized pairs;\N\item[5.] ACC+LSS for MLD of generalized pairs implies the termination of flips of generalized pairs.\N\end{itemize}