Geometry/Topology Seminar
Ruxandra Moraru
Waterloo
Co-Higgs bundles and holomorphic Poisson structures
Abstract: Co-Higgs bundles on a complex manifold $M$ are given by pairs $(E,\phi)$ consisting of a holomorphic vector bundle $E$ on $M$ together with a Higgs field $\phi \in H^0(M,\rm{End}(E) \otimes TM)$ such that $\phi \wedge \phi = 0$. They correspond to generalized holomorphic bundles on complex manifolds. They also give rise to a special class of holomorphic Poisson structures on the projective bundles $\mathbb{P}(E)$. Co-Higgs bundles were first studied by S. Rayan on Riemann surfaces and $\mathbb{CP}^2$. M. Matviichuk has more recently found necessary conditions on the Higgs fields $\phi$ for the corresponding holomorphic Poisson structures on $\mathbb{P}(E)$ to be integrable. In this talk, we consider co-Higgs bundles on compact holomorphic Poisson surfaces. We describe some of their moduli and discuss how the properties of the Higgs fields reflect those of corresponding holomorphic Poisson structures. This is joint work with Eric Boulter and Brady Ali Medina.
There will be a seminar lunch at 1 p.m. - please email schapos@uic.edu if you'd like to join.
Wednesday April 24, 2024 at 3:00 PM in 636 SEO