Moduli of tensor stable points and refined representations

Tarig Abdelgadir (ICTP Trieste)

Wednesday 30th January 16:00-17:00 Maths 311B

Abstract

Moduli spaces are a fruitful way of studying a given abelian category, take for example the moduli of point-like objects in non-commutative projective spaces or the moduli of representations of the McKay quiver. These examples yield moduli varieties, elliptic curves and minimal resolutions of Kleinian singularities. Sometimes, however, the problem lends itself better to algebraic stacks as in the case of Ringel's canoncial algebras and weighted projective lines. Our guiding example in this talk will a generalisation of these, namely Geigle-Lenzing (G-L) projective spaces as defned by Herschend, Iyama, Minamoto, Opperman. We will start with a stack and a direct sum of line bundles that form a tilting bundle and recover the stack from the corresponding category of quiver representations before applying this technique to G-L spaces. This is joint work with Daniel Chan (UNSW Sydney).

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