The Picard group of the Baily–Borel compactification of the moduli space of quasi-polarized K3 surfaces and generalizations
Year: 2026
Type: article
Abstract: We investigate the Picard group of the Baily–Borel compactification of orthogonal Shimura varieties. In particular, we show that the Picard group of the Baily–Borel compactification of the moduli space of quasi-polarized K3 surfaces is isomorphic to ℤ. Notably, this contrasts with the moduli space of smooth curves, whose natural compactification has a more complicated Picard group. More generally, we show that, for an even lattice 𝑀 of signature ( 2 , n ) (2,n) with n > 8 n>8 satisfying certain splitting conditions, the rational Picard group of Sh ̄ Γ ( M ) \overline{\operatorname{Sh}}_{\Gamma}(M) has dimension 1 when Γ contains the stable orthogonal group. The obstruction space that governs the extension of Heegner divisors on orthogonal Shimura varieties to the boundary can be identified with the space spanned by certain theta series. The central argument of our proof is to show that this space is maximal under our conditions.
Authors: Chenxin Huang, Zhiyuan Li, Manuel K.-H. Müller, Zelin Ye
Institutions: Fudan University, Sapienza University of Rome
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404648525