PreprintCC BY-NC-ND 4.0HAL
Neighborhoods of singular elliptic curves and the Riemann-Hilbert correspondence at infinity
Abstract
In his thesis work, the first author studies neighborhoods of singular elliptic curves of type I0* (Kodaira’s classification) and provides the analytic classification. This is related via a double covering construction to the analytic invariants found by Touzet, Voronin and the second author for the analytic classification of neighborhoods of smooth elliptic curves. After recalling these constructions, we explain in this note how this construction is conjecturally related to the Riemann-Hilbert correspondence at infinity for Painlevé VI case when considering neighborhood of Okamoto divisor.
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BibTeX
@misc{espejoramos2026neighborhoods,
title = {{Neighborhoods of singular elliptic curves and the Riemann-Hilbert correspondence at infinity}},
author = {Gibran Espejo-Ramos and Frank Loray and Laura Ortiz-Bobadilla},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31799},
eprint = {2609.31799},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05762274v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Neighborhoods of singular elliptic curves and the Riemann-Hilbert correspondence at infinity
AU - Gibran Espejo-Ramos
AU - Frank Loray
AU - Laura Ortiz-Bobadilla
PY - 2026
DA - 2026/09/24
PB - HAL
DO - 10.48550/arxiv.2609.31799
UR - https://hal.science/hal-05762274v1
AB - In his thesis work, the first author studies neighborhoods of singular elliptic curves of type I_0^* (Kodaira’s classification) and provides the analytic classification. This is related via a double covering construction to the analytic invariants found by Touzet, Voronin and the second author for the analytic classification of neighborhoods of smooth elliptic curves. After recalling these constructions, we explain in this note how this construction is conjecturally related to the Riemann-Hilbert correspondence at infinity for Painlevé VI case when considering neighborhood of Okamoto divisor.
ER -