Geometric Analysis and Topology Seminar

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Euler Characteristic Inequality and Rigidity of Holomorphic Covers

Speaker: Chikako Mese, Johns Hopkins

Location: Warren Weaver Hall 512

Date: Friday, October 9, 2026, 11 a.m.

Synopsis:

Harmonic map methods in holomorphic rigidity problems can lead to a finite branched holomorphic map between complex manifolds. When is this map a biholomorphism? Motivated by this question, we establish a higher-dimensional analogue of the Riemann–Hurwitz inequality for open curves. Under a positivity assumption on the logarithmic cotangent bundle of the target, the inequality relates the Euler characteristics of the source and target to the degree of the map. It yields a rigidity theorem: when the target has strictly positive signed Euler characteristic, a finite cover preserving Euler characteristic must be an isomorphism. We discuss the geometric ideas behind the proof and discuss applications to moduli spaces of curves. This is joint work with Donu Arapura and Deepam Patel.