Rigidity of modular morphisms via Fujita decomposition

Codogni, Giulio; González Alonso, Víctor; Torelli, Sara

doi:10.2140/ant.2025.19.1671

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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

DOI: 10.2140/ant.2025.19.1671

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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Vol. 19, No. 9, 2025