KASS seminar

Abstract: Central problems in complex and algebraic geometry are the existence of special Kähler metrics and the construction of moduli spaces parameterizing complex projective varieties.

While both problems are open in full generality, the Yau–Tian–Donaldson conjecture predicts that one needs to impose some sort of algebro-geometric or analytic stability conditions on the varieties.

In this talk, we discuss this problem from the point of view of families of polarized varieties over the punctured disk, where the minimization of the degree of the Chow–Mumford (CM) line bundle can be seen as a sufficient numerical criterion for the separatednes of moduli spaces of manifolds admitting special Kähler metrics.

Ultimately, we present a result on equivariant CM minimization for extremal manifolds, generalizing a result by Hattori.