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SUMMARY:K-moduli of a family of conic bundle threefolds - Kristin DeVlemin
 g (University of Massachusetts)
DTSTART:20240517T091500Z
DTEND:20240517T101500Z
UID:TALK214417@talks.cam.ac.uk
DESCRIPTION:Recently\, there has been significant progress in understandin
 g the K-moduli spaces of Fano varieties and log Fano pairs (X\,cD). When D
  is a rational multiple of the anticanonical divisor of X\, the K-moduli s
 paces of log Fano pairs (X\,cD) admit a wall crossing framework as c varie
 s and there is a finite collection of rational values of c where the K-mod
 uli spaces change. With Lena Ji\, Patrick Kennedy-Hunt\, and Ming Hao Quek
 \, we explore the K-moduli spaces in an example where D is not proportiona
 l to the anticanonical divisor. We study the K-moduli space of pairs (P1xP
 2\, cD) where D is a (2\,2) divisor and prove that there is exactly one ir
 rational value of c where the moduli spaces change. We further relate thes
 e moduli spaces to several related spaces: the GIT of (2\,2) divisors in P
 1xP2\, K-moduli of the&nbsp\;conic&nbsp\;bundle&nbsp\;threefold that is th
 e double cover of P1xP2 branched over D\, and various moduli spaces of qua
 rtic plane curves arising as the discriminant of these&nbsp\;conic&nbsp\;b
 undles.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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