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DTSTAMP:20220119T003645Z
UID:20220118T233645-0861029139@www.mn.uio.no
DTSTART:20220120T131500Z
DTEND:20220120T150000Z
LOCATION:NHA B1120
DESCRIPTION:Hilbert schemes of points for a surface are a well studied subject with many famous results like Göttsche’s formula for its Betti numbers. A natural generalization comes from studying Grothendieck’s Quot-schemes and the associated enumerative invariants. Unlike the former, punctual Quot-schemes are smooth only virtually admitting perfect obstruction theories and virtual fundamental classes. This has recently been used to study invariants counting zero-dimensional quotients of trivial vector bundles by multiple authors who used virtual localization and therefore could not treat the case of a general vector bundle. We rely on other techniques which use a general wall-crossing framework of D. Joyce to study these. Our methods rely on existence of a Lie algebra coming from vertex algebras constructed out of topological data. I will explain how these arise naturally in the Quot-scheme setting and how one can obtain explicit invariants and study their symmetries.
SUMMARY:Arkadij Bojko (ETH Zürich): Wall-crossing for punctual Quot-schemes
URL:https://www.mn.uio.no/math/english/research/groups/algebra/events/seminars/2022/bojko.html
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