𝐴_{∞}-structures associated with pairs of 1-spherical objects and noncommutative orders over curves

Polishchuk, Alexander

doi:10.1090/tran/8140

$A_\infty$-structures associated with pairs of $1$-spherical objects and noncommutative orders over curves
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Trans. Amer. Math. Soc. 373 (2020), 6029-6093 Request permission

Abstract:

We show that pairs $(X,Y)$ of $1$-spherical objects in $A_\infty$-categories, such that the morphism space $\operatorname {Hom}(X,Y)$ is concentrated in degree $0$, can be described by certain noncommutative orders over (possibly stacky) curves. In fact, we establish a more precise correspondence at the level of isomorphism of moduli spaces which we show to be affine schemes of finite type over ${\Bbb Z}$.

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