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X-FROM-URL:https://eom.sdu.dk/events/ical/c6b159cb-5343-4a59-ae6a-62a1b9aa
 5a2c
X-WR-CALNAME:QM Research Seminar: A measure on the supermoduli space with 
 Ramond punctures
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TZID:Europe/Copenhagen
X-LIC-LOCATION:Europe/Copenhagen
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DTSTAMP:20260602T163438Z
DTSTART:20261028T030000
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DESCRIPTION:[b]Speaker: Nadia Ott [/b](University of Southern Denmark) \n\
 n[b]Abstract: [/b]​An essential ingredient in perturbative string theory 
 is a certain measure on the moduli space Mg of curves. This measure is de
 fined in terms of the Mumford isomorphism\, which relates the canonical l
 ine bundle on Mg to the determinant of cohomology of the pushforward of t
 he relative canonical line bundle on the universal curve. This pushforwar
 d\, and thus also its determinant\, has a natural hermitian metric given 
 by integration. This metric can be expressed in terms of the period map.\
 n​For superstring theory\, this generalizes to a measure on the supermodu
 li space Mg. The super Mumford isomorphism relates the canonical bundle o
 n Mg to the fifth power of the Berezinian of the pushforward of the relat
 ive canonical bundle on the universal supercurve. However\, in the super 
 case\, there is no Hermitian metric given by integration. Instead\, the m
 etric is defined in terms of the period map. Furthermore\, in contrast to
  the classical case\, the super period map is non-holomorphic and develop
 s a pole along the bad locus. Deligne recently proved that the supermeasu
 re extends smoothly over the bad locus.\n​In joint work with Ron Donagi\,
  we define a measure on Mg\,0\,2r\, the supermoduli space with Ramond pun
 ctures\, using the super Mumford isomorphism and super period map\, adapt
 ed to the case of Ramond punctures. We show that in Mg\,0\,2r\, the analo
 gous bad locus has codimension 2 or higher for r > 1\, allowing us to ext
 end the measure using a Hartog-like argument.
DTEND:20241022T140000Z
DTSTAMP:20260602T163438Z
DTSTART:20241022T130000Z
LOCATION:Syddansk Universitet\, Campusvej 55\, 5230\, Odense M
SEQUENCE:0
SUMMARY:QM Research Seminar: A measure on the supermoduli space with Ramon
 d punctures
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