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9. Line bundles over toric stacks

    1.     [Wang, Borisov-Wang]: Found a condition on underlying fan for a toric stack to admit infinitely many acyclic line bundles (meaning $\mathcal{L}$ with $H^*(\mathcal{L})=0$ for all $*$, e.g. $\mathcal{O}(-1)$ on $\mathbb{P}^n$) (e.g. in $2D$ if fan has collinear rays).

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      Problem 9.1.

      1. Understand symplectic mirror of these criteria.
      2. Understand consequences of generalizations of these critera (e.g. if there exists a toric subvariety whose fans is contained in a linear subspace) or if generalized.

          Cite this as: AimPL: Syzygies and mirror symmetry, available at http://aimpl.org/syzygyms.