# Moduli of noncommutative Hirzebruch surfaces

@article{Mori2019ModuliON, title={Moduli of noncommutative Hirzebruch surfaces}, author={Izuru Mori and Shinnosuke Okawa and Kazushi Ueda}, journal={arXiv: Algebraic Geometry}, year={2019} }

We introduce three non-compact moduli stacks parametrizing noncommutative deformations of Hirzebruch surfaces; the first is the moduli stack of locally free sheaf bimodules of rank 2, which appears in the definition of noncommutative $\mathbb{P}^1$-bundle in the sense of Van den Bergh arXiv:math/0102005, the second is the moduli stack of relations of a quiver in the sense of arXiv:1411.7770, and the third is the moduli stack of quadruples consisting of an elliptic curve and three line bundles…

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