Rank 2 quasiparabolic vector bundles on P¹ and the variety of linear subspaces contained in two odd-dimensional quadrics

الأصل · EN

Let N be the moduli space of stable rank 2 quasiparabolic vector bundles of fixed degree on the projective line with 2g+1 marked points, where g>1, and stability is with respect to the weights 0,1/2 at each marked point. In this note we show that N is isomorphic to the variety of (g-2)-dimensional linear subspaces of P²ᵍ, contained in the intersection of two quadrics. The proof relies on the work of Bhosle on the relation among quasiparabolic vector bundles on P¹ and invariant vector bundles on hyperelliptic curves, and the description by Bhosle and Ramanan of the moduli space of stable rank 2 vector bundles on a hyperelliptic curve, with fixed determinant of odd degree.