Asymptotic behaviour of the Hitchin metric on the moduli space of Higgs bundles
Takuro Mochizuki
The moduli space of stable Higgs bundles of degree 0 is equipped with the hyperkähler metric, called the Hitchin metric. On the locus where the Hitchin fibration is smooth, there is the hyperkähler metric called the semi-flat metric, associated with the algebraic integrable systems with the Hitchin section. We prove the exponentially rapid decay of the difference between the Hitchin metric and the semi-flat metric along the ray (E,tθ) as t→∞.
Subjects: Differential Geometry (math.DG); Algebraic Geometry (math.AG)
MSC classes: 53C07, 58E15, 14D21, 81T13
Cite as: arXiv:2305.17638 [math.DG]