Visible Lagrangians for Hitchin Systems and Pillowcase Covers
Algebraic Geometry
2026-03-11 v3 Geometric Topology
Abstract
We study complex Lagrangians in Hitchin systems that factor through a proper subvariety of the Hitchin base non-trivially intersecting the regular locus. This gives a general framework for several examples in the literature. We compute the fiber-wise Fourier-Mukai transform of flat line bundles on visible Lagrangians. This proposes a construction of mirror dual branes to visible Lagrangians. Finally, we study a new example of visible Lagrangians in detail. Such visible Lagrangian exists whenever the underlying Riemann surface is a pillowcase cover. The proposed mirror dual brane turns out to be closely related to Hausel's toy model.
Keywords
Cite
@article{arxiv.2310.15716,
title = {Visible Lagrangians for Hitchin Systems and Pillowcase Covers},
author = {Johannes Horn and Johannes Schwab},
journal= {arXiv preprint arXiv:2310.15716},
year = {2026}
}