PreprintCC BY 4.0arXiv
Moduli space of irregular singular λ-connections and the relative symplectic form
Abstract
We study the moduli space of λ-connections with ramified singularities on a smooth projective curve X. We construct a quasi-projective relative moduli scheme MαHod → Λ of α-stable λ-connections over a base parameter space Λ. This moduli space connects the irregular de Rham moduli space (λ=1) and the irregular Dolbeault moduli space of Higgs bundles equipped with non-zero irregular local exponents (λ=0). Furthermore, we show that MαHod is smooth over Λ and carries a canonical relative symplectic form ωMαHod/Λ, yielding a natural Poisson structure on the total space.
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BibTeX
@misc{inaba2026moduli,
title = {{Moduli space of irregular singular $λ$-connections and the relative symplectic form}},
author = {Michi-aki Inaba and Arata Komyo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40352},
eprint = {2610.40352},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40352},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Moduli space of irregular singular λ-connections and the relative symplectic form
AU - Michi-aki Inaba
AU - Arata Komyo
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40352
UR - https://arxiv.org/abs/2610.40352
AB - We study the moduli space of λ-connections with ramified singularities on a smooth projective curve X. We construct a quasi-projective relative moduli scheme M^α_Hod → Λ of α-stable λ-connections over a base parameter space Λ. This moduli space connects the irregular de Rham moduli space (λ=1) and the irregular Dolbeault moduli space of Higgs bundles equipped with non-zero irregular local exponents (λ=0). Furthermore, we show that M^α_Hod is smooth over Λ and carries a canonical relative symplectic form ω_M^α_Hod/Λ, yielding a natural Poisson structure on the total space.
ER -