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SUMMARY:K-moduli for log Fano complete intersections - Theo Papazachariou\
 , Essex
DTSTART:20211020T131500Z
DTEND:20211020T141500Z
UID:TALK164266@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:An important category of geometric objects in algebraic geomet
 ry is smooth Fano varieties\, which have positive curvature. These have be
 en classified in 1\, 8 and 105 families in dimensions 1\, 2 and 3 respecti
 vely\, while in higher dimensions the number of Fano families is yet unkno
 wn\, although we know that their number is bounded. An important problem i
 s compactifying these families into moduli spaces via K-stability. In this
  talk\, I will describe the compactification of the family of Fano threefo
 lds\, which is obtained by blowing up the projective space along a complet
 e intersection of two quadrics\, into a K-moduli space using Geometric Inv
 ariant Theory (GIT). A more interesting setting occurs in the case of pair
 s of varieties and a hyperplane section where the K-moduli compactificatio
 ns tessellate depending on a parameter. In this case it has been shown rec
 ently that the K-moduli decompose into a wall-chamber decomposition depend
 ing on a parameter\, but wall-crossing phenomena are still difficult to de
 scribe explicitly.  Using GIT\, I will describe an explicit example of wal
 l-crossing in the K-moduli spaces\, where both variety and divisor differ 
 in the deformation families before and after the wall\, given by log pairs
  of Fano surfaces of degree 4 and a hyperplane section. 
LOCATION:CMS MR13
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