UC San Diego
Algebraic Geometry
Seminar
Algebraic Geometry
Seminar
Organizers: Kristin DeVleming, Elham Izadi, James McKernan, Fanjun Meng, Dragos Oprea.
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Abstract: Arising in the construction of ramified double-covers of Fano varieties, as well as the investigation of Fano four-folds, Casagrande-Druel varieties are conic bundles $Y$ realized as certain blow-ups of projective bundles over their base $V$ with discriminant locus $B$. These varieties are Fano under minor additional assumptions.
We show that a Casagrande-Druel variety $Y$ satisfying an additional proportionality condition, is K-poly/semistable if and only if the pair $(V,aB)$ is K-poly/semistable for an explicit coefficient $a$, and that Casagrande-Druel variety failing this proportionality condition is K-unstable. Using this we then construct the K-moduli spaces of Casagrande-Druel varieties by directly relating the K-moduli of such Fano varieties to the K-moduli spaces of the base pairs $(V,aB)$.
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