## University of Sydney Algebra Seminar

# Daniel Chan (University of New South Wales)

## Friday 28th February, 12:05-12:55pm, Place: Carslaw 454

### Serre stable representations of the canonical algebra

In 1978, Beilinson made a remarkable discovery connecting algebraic geometry to the theory of finite dimensional algebras. He showed that the derived category of projective space was equivalent to the derived category of some finite dimensional algebra. Many more such derived equivalences have since been found, including between certain stacky versions of the projective line known as weighted projective lines and canonical algebras. It was noted that given such a derived equivalence between a projective variety and a finite dimensional algebra A, the variety could often be recovered as a moduli space of A-modules via geometric invariant theory. This approach fails in the case of the canonical algebra. We introduce a new moduli stack of Serre stable modules and show that this does recover the weighted projective line when applied to the canonical algebra. This is a report on joint ongoing work with Boris Lerner.