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Noncommutative resolution of $SU_C(2)$

Event Category:
Reading Seminar in Algebraic Geometry
Elias Sink

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 $g\geq 2$ 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 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 $C$. This result provides evidence towards the longstanding expectation that $SU_C(2)$ is rational.

Friday, May 10, 2024 - 2:30pm
LGRT 1685