Algebra and Geometry Seminar
Matrix factorization plays an important role in mathematics and it is interesting to consider matrix factorizations with coherent components over non-affine spaces. On difficulty is that it is quite complicated to describe quasi-isomorphisms between them. On the other hand, people showed that the category of flat anti-holomorphic superconnections is equivalent to the bounded derived category of coherent sheaves on complex manifolds, which assures us that superconnection is a useful tool in the study of coherent sheaves. In this talk I will describe an attempt to use (non-flat) anti-holomorphic superconnections to give resolutions of coherent matrix factorizations and some possible applications along this line.