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Lc pairs are fundamental objects in the minimal model theory,ÌýandÌýa non-normal analogue of lc pairs, called semi-log canonical (slc, forÌýshort)Ìýpairs, are important objects in the moduli problem and inductiveÌýarguments in the minimal model theory.ÌýIn the birational geometry, a lot of theorems for lc pairs are reducedÌýtoÌýthe statements of dlt pairs by using a birational model called a dltÌýblow-up.ÌýCompared to lc pairs, dlt pairs have good properties.ÌýTherefore, it is natural to consider an analogous statement of theÌýexistence ofÌýdlt blow-ups holds for slc pairs.ÌýThe notion of semi-divisorial log terminal (sdlt, for short) pairs wasÌýdefinedÌýsimilarly to the case of dlt pairs, and a question on the existence ofÌýsdlt blow-ups for specialÌýslc pairs was raised by János Kollár.

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