CoHAs of Weighted Projective Lines |
Timm Peerenboom |
Freitag, 7. Februar 2025 10:30Uhr |
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The Cohomological Hall Algebra (CoHA), introduced by Kontsevich--Soibelman, is a cohomological analogue of the Ringel--Hall algebra. While for a symmetric quiver this algebra is free (super) symmetric, there were essentially no other examples that were known explicitly in terms of generators and relations, until Franzen--Reineke computed the CoHA of (regular representations) of the 2-Kronecker quiver. The 2-Kronecker quiver is derived equivalent to the projective line and regular representations correspond to torsion sheaves; thus Franzen--Reineke's algebra can also be seen as the CoHA of torsion sheaves on $\mathbb{P}^1$. We extend this computation to CoHAs of torsion sheaves on the so-called weighted projective lines. As a special case, we also obtain the CoHAs of regular representations of all other extended Dynkin quivers (satisfying a certain natural condition on the Euler form). |