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SUMMARY:Giovanni Inchiostro (University of Washington)
DTSTART:20230323T223000Z
DTEND:20230323T233000Z
DTSTAMP:20260422T053626Z
UID:SFUQNTAG/84
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SFUQNTAG/84/
 ">Wall crossing morphisms for moduli of stable pairs</a>\nby Giovanni Inch
 iostro (University of Washington) as part of SFU NT-AG seminar\n\nLecture 
 held in AQ 4140.\n\nAbstract\nConsider a quasi-compact moduli space M of p
 airs (X\,D) consisting of a variety X and a divisor D on X. If M is not pr
 oper\, it is reasonable to find a compactification of it. Assume furthermo
 re that there are two rational numbers $0 \\lt b \\lt a\\lt 1$ such that\,
  for every pair (X\,D) corresponding 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 stable 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 two compactifications. The main result
  is that\, up to replacing M_a and M_b with their normalizations\, there a
 re birational morphisms $M_a \\to M_b$\, recovering Hassett's result (for 
 the case of curves) in all dimensions. If time permits\, I will explain a 
 slight variation of the moduli functor of varieties with pairs\, which has
  a particularly accessible moduli functor\, leads to a simple proof of the
  projectivity of the moduli of stable pairs\, and conjecturally leads to b
 etter wall-crossing phenomena. The talk will be based on my work with Kenn
 y Ascher\, Dori Bejleri\, Zsolt Patakfalvi\; and my work with Stefano Fili
 pazzi.\n
LOCATION:https://researchseminars.org/talk/SFUQNTAG/84/
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