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SUMMARY:Andrea Petracci (FU Berlin)
DTSTART:20200827T123000Z
DTEND:20200827T133000Z
DTSTAMP:20260423T005758Z
UID:notts_ag/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/notts_ag/22/
 ">$K$-moduli stacks and $K$-moduli spaces are singular</a>\nby Andrea Petr
 acci (FU Berlin) as part of Online Nottingham algebraic geometry seminar\n
 \n\nAbstract\nOnly recently a separated moduli space for (some) Fano varie
 ties has been constructed by several algebraic geometers: this is the $K$-
 moduli stack which parametrises $K$-semistable Fano varieties and has a se
 parated good moduli space. A natural question is: are these stacks and spa
 ces smooth? This question makes sense because deformations of smooth Fano 
 varieties are unobstructed\, so moduli stacks of smooth Fano varieties are
  smooth. In this talk I will explain how to use toric geometry to construc
 t examples of non-smooth points in the $K$-moduli stack and the $K$-moduli
  space of Fano $3$-folds. This is joint work with Anne-Sophie Kaloghiros.\
 n
LOCATION:https://researchseminars.org/talk/notts_ag/22/
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