Full Exceptional Sequence for a Fine Quiver Moduli Space

Svetlana Makarova; Junyu Meng

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arXiv · 2412.15390

Full Exceptional Sequence for a Fine Quiver Moduli Space

Svetlana Makarova·Junyu Meng

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Abstract

We consider the fine quiver moduli space of representations of the 3-Kronecker quiver of dimension vector $(2,3)$, which is a blow down of the Hilbert scheme of 3 points on $\mathds{P}^2$. A short description of its geometry and Chow ring is given. Then we exhibit an exceptional sequence for the derived category by understanding a $\mathds{P}^1$-bundle over it and using Teleman Quantization. The fullness of the exceptional sequence is proved by using a covering argument and computations of mutations.

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Svetlana Makarova, Junyu Meng. 2024-12-19. Full Exceptional Sequence for a Fine Quiver Moduli Space. https://arxiv.org/abs/2412.15390

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