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DTSTAMP:20220526T012238Z
UID:20220525T232238-0861029139@www.mn.uio.no
DTSTART:20220120T131500Z
DTEND:20220120T150000Z
LOCATION:NHA B1120
DESCRIPTION:Hilbert schemes of points for a surface are a well studied sub
ject with many famous results like Göttsche’s formula for its Betti numbe
rs. A natural generalization comes from studying Grothendieck’s Quot-sche
mes and the associated enumerative invariants. Unlike the former, punctua
l Quot-schemes are smooth only virtually admitting perfect obstruction th
eories and virtual fundamental classes. This has recently been used to st
udy invariants counting zero-dimensional quotients of trivial vector bund
les by multiple authors who used virtual localization and therefore could
not treat the case of a general vector bundle. We rely on other techniqu
es 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 ar
ise 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-scheme
s
URL:https://www.mn.uio.no/math/english/research/groups/algebra/events/semi
nars/2022/bojko.html
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