Noncommutative resolution of SUC(2)

We study the derived category of the moduli space 𝑆𝑈_𝐶(2) of rank 2 vector bundles on a smooth projective curve 𝐶 of genus 𝑔 ≥ 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 𝑆𝑈_𝐶(2) as a subcategory 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 𝐶. This result provides evidence towards the longstanding expectation that 𝑆𝑈_𝐶(2) is rational.