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SUMMARY:Wild level structures and Hurwitz spaces [Seminar Algebraic Geomet
 ry (SAG)]
DTSTART:20260625T083000Z
DTEND:20260625T093000Z
DTSTAMP:20260719T030400Z
UID:indico-event-1174@math-events.uni-bonn.de
DESCRIPTION:Speakers: Michael Temkin\n\nHurwitz moduli spaces of smooth (a
 nd stable) curves are classical and well studied objects when the order of
  ramification is invertible. Up to now very little was known about the wil
 d case. In particular\, Abramovich--Oort described in 2000 a natural model
  over Z (with 2 non-inverted) of the classical space of double covers 
 of the projective line ramified at four points. Already this case turned o
 ut to be quite mysterious and lacked a modular interpretation. In particul
 ar\, this space turned out to be the blowing up of the Katz-Mazur modular 
 curve X(2) at the supersingular point.\nIn my talk I will discuss this e
 xample in some detail and then will outline two modern continuations of th
 is story:\n\nA work of Hippold\, where a moduli space of degree-p covers w
 as constructed over Z[1/(p−1)!]\, including the example of [AO]\, and w
 as proved to be log smooth over (Z[1/(p−1)!]\,log(p)) in quite a few c
 ases.\nMy work in progress where a new modular model over Z of the class
 ical level-N modular curve is constructed. It classifies stable N2-pointe
 d genus-1 curves with an action of (Z/NZ)2 acting transitively on the ma
 rked points and satisfying some natural restrictions which ensure liftabil
 ity to an elliptic curve with marked N-torsion. The new modular model is 
 obtained from Katz-Mazur model as the minimal normal modification which se
 parates all ordinary branches at the supersingular points.\n\n\nhttps://ma
 th-events.uni-bonn.de/event/1174/
URL:https://math-events.uni-bonn.de/event/1174/
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