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SUMMARY:Wall crossing morphisms for moduli of stable pairs - Giovanni Inch
 iostro\, University of Washington
DTSTART:20231011T131500Z
DTEND:20231011T141500Z
UID:TALK203305@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:Consider a quasi-compact moduli space M of pairs (X\,D) consis
 ting of a variety X and a divisor D on X. If M is not proper\, it is reaso
 nable to find a compactification of it. Assume furthermore that there are 
 two rational numbers 0<b<a<1 such that\, for every pair (X\,D) correspondi
 ng to a point in M\, the pair (X\,D) is smooth and normal crossings\, and 
 the Q-divisors K_X+aD and K_X+bD are ample. Using Kollár's formalism of s
 table pairs\, one can construct two different compactifications of M (M_a 
 and M_b)\, corresponding to a and b. I will explain how to relate these tw
 o compactifications. The main result is that\, up to replacing M_a and M_b
  with their normalizations\, there are birational morphisms M_a \\to M_b\,
  recovering Hassett's result (for the case of curves) in all dimensions. I
 f time permits\, I will explain a slight variation of the moduli functor o
 f varieties with pairs\, which has a particularly accessible moduli functo
 r\, leads to a simple proof of the projectivity of the moduli of stable pa
 irs\, and conjecturally leads to better wall-crossing phenomena. The talk 
 will be based on my work with Kenny Ascher\, Dori Bejleri\, Zsolt Patakfal
 vi\; and my work with Stefano Filipazzi.
LOCATION:CMS MR13
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