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4. Clarifying and Expanding Toric Mirror Symmetry


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      Problem 4.1.

      [John Cobb] How do the choices of stop data in the cotangent bundle relate to the choices of the irrelevant ideal in the Cox ring?


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          Problem 4.2.

          [Jeff Hicks] Given a choice of a mirror skeleton, one can consider its canonical probe generators. What is the geometric meaning of the mutated collection of these generators? Can we find another skeleton for the same symplectic manifold, whose canonical generators are the mutated collection?


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              Problem 4.3.

              [David Favero] Does Morelli’s algebro-geometric cobordism in the context of weak factorizations have a mirror interpretation? What about elementary cobordism?


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                  Problem 4.4.

                  [Maxim Jeffs] What is the algebro-geometric "mirror" to Pontryagin classes of Lagrangians in $(T^{*}\mathbb{T}^n)$?


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                      Problem 4.5.

                      [Reginald Andrerson] Are there quiver-theoretic descriptions of certain moduli of sheaves (e.g $Hilb_{n}$ on toric varieties) via resolutions by the Bondal-Thompsen collection?


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                          Problem 4.6.

                          [Reginal Anderson] Is Bondal-Thompsen collection related to Bridgeland stability conditions?

                              Cite this as: AimPL: Homological mirror symmetry and multigraded commutative algebra, available at http://aimpl.org/hmsandmga.