arXiv subjects
Publications and source records attributed to Wei Tseu.
We reinvestigate the problem of describing the Fourier-Mukai kernel for the derived equivalence associated to a stratified Mukai flop. For the case of Grassmannians of planes we give a very simple geometric construction of the kernel, using the framework of matrix factorizations.
We identify two distinct approaches to the derived equivalence for the stratified Mukai flop of cotangent bundles of Grassmannians -- one induced by the geometric categorical sl(2) action, and the other through the magic window category of graded matrix factorizations on the gauged Landau-Ginzburg model -- via the Kn\"orrer periodicity.
We present an explicit construction of tilting bundles on cotangent bundles of Grassmannians of 2-planes. This construction is based on Kapranov's exceptional collection for the underlying Grassmannians, and utilizes specific iterative extensions. The resulting tilting bundle exhibits invariance under the derived equivalence for the stratified Mukai flop through the geometric categorical sl(2) action, providing a categorical lift of the K-theoretic canonical basis up to shifts.