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SUMMARY:Almost toric yoga for stable double surfaces (Part I) - Jonny Evan
 s (Lancaster)
DTSTART:20250313T111500Z
DTEND:20250313T121500Z
UID:TALK228205@talks.cam.ac.uk
CONTACT:Ailsa Keating
DESCRIPTION:(This is part I of a series of two talks.) The moduli space of
  surfaces of general type has a natural compactification where the boundar
 y points correspond to ``stable surfaces''. If we restrict attention to su
 rfaces which are branched double covers of certain simple surfaces (like t
 he projective plane or a Hirzebruch surface) then singularities can develo
 p in three ways: the branch curve can degenerate\, or the base surface can
  degenerate\, or the branch curve and the base surface can develop singula
 rities at the same point. If the limit of the base surface is toric\, one 
 can use toric geometry to understand the stable limit of the double cover\
 , but often degenerations of the plane or a Hirzebruch surface are only *a
 lmost* toric (in a precise sense). Thanks to work of Gross\, Hacking and K
 eel\, the same diagrammatic techniques that work for toric degenerations c
 an be applied in this setting\, and one can use this to get a full classif
 ication of normal stable surfaces for some components of the moduli space.
  I will explain how this works for octic double planes. This is based on j
 oint work with Angelica Simonetti and Giancarlo Urzua.
LOCATION:CMS\, MR14
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