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Rigidity of modular morphisms via Fujita decomposition

Giulio Codogni, Víctor González Alonso and Sara Torelli

Vol. 19 (2025), No. 9, 1671–1683
Abstract

We prove that the Torelli, Prym and spin-Torelli morphisms, as well as covering maps between moduli stacks of smooth projective curves, cannot be deformed. The proofs use properties of the Fujita decomposition of the Hodge bundle of families of curves.

Keywords
moduli spaces, rigidity of period maps, Fujita decomposition, curves, abelian varieties
Mathematical Subject Classification
Primary: 14H10
Secondary: 32G20
Milestones
Received: 16 May 2023
Revised: 11 July 2024
Accepted: 13 September 2024
Published: 21 July 2025
Authors
Giulio Codogni
Dipartimento di Matematica
Università di Roma Tor Vergata
Rome
Italy
Víctor González Alonso
Institut für Algebraische Geometrie
Leibniz Universität
Hannover
Germany
Sara Torelli
Department of Mathematics “Giuseppe Peano”
Università di Torino
Torino
Italy

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