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Let N be the moduli space of stable rank 2 quasiparabolic vector bundles offixed degree on the projective line with 2g+1 marked points, where g>1, andstability is with respect to the weights {0,1/2} at each marked point. In thisnote we show that N is isomorphic to the variety of (g-2)-dimensional linearsubspaces of P^{2g}, contained in the intersection of two quadrics. The proofrelies on the work of Bhosle on the relation among quasiparabolic vectorbundles on P^1 and invariant vector bundles on hyperelliptic curves, and thedescription by Bhosle and Ramanan of the moduli space of stable rank 2 vectorbundles on a hyperelliptic curve, with fixed determinant of odd degree.

Rank $2$ quasiparabolic vector bundles on $\mathbb{P}^1$ and the variety of linear subspaces contained in two odd-dimensional quadrics