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We study birational geometry of the moduli space of stable sheaves on aquadric surface with Hilbert polynomial $5m + 1$ and $c_{1} = (2, 3)$. Wedescribe a birational map between the moduli space and a projective bundle overa Grassmannian as a composition of smooth blow-ups/downs.

Birational geometry of the moduli space of pure sheaves on quadric surface