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1. Computational and structural aspects of resolutions


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      Problem 1.1.

      [Daniel Erman] When do resolutions of toric subvarieties from the work of Hanlon-Hicks-Lazarev (and their minimizations) have nice properties? More specifically, when is the resolution of the torus fixed point projectively normal? When is the resolution of the diagonal symmetric?


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          Problem 1.2.

          [Michael Brown] Given a coherent sheaf $F$ on a toric variety $X$ (or a complex of sheaves), can we implement a code in M2 that computes its free monad in Bondal-Thompsen collection?


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              Problem 1.3.

              [Mykola Sapronov] Can we implement algorithms in M2 to do computations over non-commutative algebras?

                •     The minimal resolution of normalizations of toric ideals need not be cellular.

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                  Problem 1.4.

                  [Jay Yang] Can we give topological/combinatorial criteria for when the minimal resolution of a toric ideal is cellular?

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