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Title:
On local volumes and boundedness of singularities
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Abstract:
A folklore conjecture predicts that the set of local volumes of klt singularities is discrete away from zero (resp. satisfies ACC) if the coefficients of the boundary divisors belong to a finite (resp. DCC) set. In this talk, we will prove this conjecture when the ambient spaces are analytically bounded. We will also explore the relation between local volumes, log canonical thresholds and certain boundedness conditions related to \epsilon-plt blow-ups. This is based on ongoing joint work with Jingjun Han and Yuchen Liu.
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