| Register
\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

2. Questions about Cox Category


    1. Add remark

      Problem 2.1.

      [Matthew Ballard] Can we describe and make sense of quantum cohomology of $D_{Cox}$?


        • Add remark

          Problem 2.2.

          [Michael Brown] Can we understand geometrically the Serre functor of $D_{Cox}$?


            • Add remark

              Problem 2.3.

              [Andrew Hanlon] Is there a Landau-Ginzburg mirror to $D_{Cox}?$


                • Add remark

                  Problem 2.4.

                  [Mahrud Sayrafi] Is there a notion of Koszul duality for $D_{Cox}?$.


                    • Add remark

                      Problem 2.5.

                      [Jesse Huang] Given a wall in the secondary fan, one can consider a sub-GIT problem with the corresponding $D_{Cox}$ category. Is there a functorial relationship between these $D_{Cox}$ categories?


                        • Add remark

                          Problem 2.6.

                          Do there exist analogs of $D_{Cox}$ for other spaces?

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