Constructing co-Higgs Bundles in Higher Dimensions

          @misc{ scivideos_PIRSA:12050030,
            doi = {10.48660/12050030},
            url = {https://pirsa.org/12050030},
            author = {Rayan, Steven},
            keywords = {},
            language = {en},
            title = {Constructing co-Higgs Bundles in Higher Dimensions},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2012},
            month = {may},
            note = {PIRSA:12050030 see, \url{https://scivideos.org/index.php/pirsa/12050030}}
          }
          

Abstract

I will outline a couple of constructions of co-Higgs bundles, which are holomorphic vector bundles with Higgs fields taking values in the tangent bundle. One reason why these objects are interesting is that they are precisely the generalized holomorphic bundles on an ordinary complex manifold considered as a generalized complex manifold. One method produces a co-Higgs bundle on any complex manifold; in a sense, this is the canonical co-Higgs bundle. The other is specifically for the projective plane. Recall that one of the earliest constructions of (interesting) vector bundles
on a complex surface was Schwarzenberger's construction of a rank-2 vector bundle on the projective plane from a double cover. I hope to breathe new life into this object by showing that the bundle carries a natural O(1)-valued Higgs field, which can be pushed to a T-valued Higgs field on P2. For both examples, we will discuss some aspects of their stability and deformation theory.