Mathematics Dept.
University of Hong Kong
Mon 20 Aug 2018, 4:00pm SPECIAL
Algebraic Geometry Seminar
Noncommutative Mather-Yau theorem and its applications
Mon 20 Aug 2018, 4:00pm-5:00pm


We prove that the right equivalence class of a super potential in complete free algebra is determined by its Jacobi algebra and the canonical class in its 0-th Hochschild homology represented by the super potential, assuming the Jacobi algebra is finite dimensional. This is a noncommutative version of the famous Mather-Yau theorem in isolated hyper surface singularities. As a consequence, we prove a rigidity theorem for Ginzburg dg-algebra. I will discuss some applications of these results in three dimensional birational geometry. This is a joint work with Guisong Zhou (1803.06128).