Geometry and Topology Seminar

Ruiran Sun, University of Toronto

Rigidity problems on moduli spaces of polarized manifolds.

Motivated by Shafarevich’s conjecture, Arakelov and Parshin established a significant finiteness result: for any curve C, the set of isomorphism classes of non-constant morphisms C → M_g is finite for g≥2. However, for moduli stacks parametrizing higher-dimensional varieties, the Arakelov-Parshin finiteness theorem fails due to the presence of non-rigid families. In this talk, I will review recent advances in rigidity problems for moduli spaces of polarized manifolds, focusing on two main topics: an "one-pointed" version of Shafarevich’s finiteness theorem and the distribution of non-rigid families within moduli spaces.

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