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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.