Resolution and logarithmic resolution via weighted blowings up
Dan Abramovich (Brown University)
Abstract: This lecture combines resolution of singularities, logarithmic geometry and algebraic stacks. I will not assume familiarity neither with resolution of singularities nor with logarithmic geometry. I report on work with Temkin and Wlodarczyk and work of Quek. Resolving singularities in families requires logarithmic geometry. Surprisingly, trying to do this canonically forces us to use stack-theoretic modifications. Surprisingly, stack-theoretic modifications provides an efficient iterative resolution method in which the worst singularities are blown up without regard to the history. Not so surprisingly, to make exceptional divisors cooperate we need logarithmic geometry again.
Audience: researchers in the topic
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More seminar information (including slides and videos, when available): agstanford.com
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