Crepant semi-divisorial terminal model

Crepant semi-divisorial terminal model

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Kenta Hashizume, The University of Tokyo

Zoom link:  https://princeton.zoom.us/j/91248028438

Lc pairs are fundamental objects in the minimal model theory, and a non-normal analogue of lc pairs, called semi-log canonical (slc, for short) pairs, are important objects in the moduli problem and inductive arguments in the minimal model theory. In the birational geometry, a lot of theorems for lc pairs are reduced to the statements of dlt pairs by using a birational model called a dlt blow-up. Compared to lc pairs, dlt pairs have good properties. Therefore, it is natural to consider an analogous statement of the existence of dlt blow-ups holds for slc pairs. The notion of semi-divisorial log terminal (sdlt, for short) pairs was defined similarly to the case of dlt pairs, and a question on the existence of sdlt blow-ups for special slc pairs was raised by János Kollár.

In this talk, I explain the existence of crepant sdlt model of slc pairs, that is a variant of sdlt blow-ups.