BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Theodoros Papazachariou (University of Essex) DTSTART:20220426T140000Z DTEND:20220426T150000Z DTSTAMP:20260423T053132Z UID:ZAG/205 DESCRIPTION:Title: K- moduli for log Fano complete intersections\nby Theodoros Papazachariou (University of Essex) as part of ZAG (Zoom Algebraic Geometry) seminar\n\ n\nAbstract\nAn important category of geometric objects in algebraic geome try is smooth Fano varieties\, which have positive curvature. These have b een classified in 1\, 10 and 105 families in dimensions 1\, 2 and 3 respec tively\, while in higher dimensions the number of Fano families is yet unk nown\, although we know that their number is bounded. An important problem is compactifying these families into moduli spaces via K-stability. In th is talk\, I will describe the compactification of the family of Fano three folds\, which is obtained by blowing up the projective space along a compl ete intersection of two quadrics which is an elliptic curve\, into a K-mod uli space using Geometric Invariant Theory (GIT). A more interesting setti ng occurs in the case of pairs of varieties and a hyperplane section where the K-moduli compactifications tessellate depending on a parameter. In th is case it has been shown recently that the K-moduli decompose into a wall -chamber decomposition depending on a parameter\, but wall-crossing phenom ena are still difficult to describe explicitly. Using GIT\, I will descri be an explicit example of wall-crossing in the K-moduli spaces\, where bot h 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 hyperplan e section.\n LOCATION:https://researchseminars.org/talk/ZAG/205/ END:VEVENT END:VCALENDAR