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We will show that the Atiyah-Bott-Goldman volumes of the quotient spaces ofthe $\mathsf{PSL}(n,\mathbb{R})$-Hitchin components by the mapping class groupare infinite if $n>2$. We use the bulge deformation of the Hitchinrepresentations and show that infinitely many images under some sequence ofdeformations are disjoint under the projection to the moduli space of Hitchinrepresentations.

The volumes of the $\text{PSL}(n, \mathbb{R})$-Hitchin-Riemann moduli spaces are infinite