PreprintarXiv licencearXiv
Normal Matrix Model and Hyperelliptic Curves
Abstract
We present a two-matrix model with a normal matrix with eigenvalues confined to contours in the upper half plane coupled to a Hermitian matrix. This generalizes the matrix model proposed by Jens Hoppe which corresponds to a single horizontal line. We solve the saddle point equations for several lines and show that the large-N free energy can be expressed in terms of hyperelliptic integrals. We show that the model describes a Coulomb gas in the presence of an infinite conducting boundary.
Related
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- A cubic Chabauty criterion for hyperelliptic curves
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- Arithmetic statistics of isogeny Selmer groups associated to hyperelliptic curves
- Number of equations defining the Kummer varieties of hyperelliptic curves
BibTeX
@misc{melin2026normal,
title = {{Normal Matrix Model and Hyperelliptic Curves}},
author = {Valdemar Melin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30475},
eprint = {2610.30475},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30475},
}
RIS
TY - UNPB
TI - Normal Matrix Model and Hyperelliptic Curves
AU - Valdemar Melin
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30475
UR - https://arxiv.org/abs/2610.30475
AB - We present a two-matrix model with a normal matrix with eigenvalues confined to contours in the upper half plane coupled to a Hermitian matrix. This generalizes the matrix model proposed by Jens Hoppe which corresponds to a single horizontal line. We solve the saddle point equations for several lines and show that the large-N free energy can be expressed in terms of hyperelliptic integrals. We show that the model describes a Coulomb gas in the presence of an infinite conducting boundary.
ER -