Resolution and logarithmic resolution via weighted blowings up

Dan Abramovich (Brown University)

31-Jul-2020, 19:30-20:30 (3 years ago)

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.

algebraic geometry

Audience: researchers in the topic

( paper | slides | video )

Stanford algebraic geometry seminar

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Organizer: Ravi Vakil*
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