Noncommutative resolution of SUC(2)

We study the derived category of the moduli space SUC(2)𝑆𝑈𝐶(2) of rank 2 vector bundles on a smooth projective curve C𝐶 of genus g≥2𝑔≥2 with trivial determinant. Unlike the case of fixed odd determinant, this moduli space is singular. Generalizing recent work of Tevelev and Torres, we construct a noncommutative resolution of singularities of SUC(2)𝑆𝑈𝐶(2) as a subcategory of the derived category of the Thaddeus' moduli space of stable pairs. We find that this category consists of blocks equivalent to the derived categories of even symmetric powers of C𝐶. This result provides evidence towards the longstanding expectation that SUC(2)𝑆𝑈𝐶(2) is rational.