In this talk, I will discuss the history and established results concerning the CR transversality problem, and share our recent progress on real hypersurfaces when the target manifold is a hyperquadric. Specifically, we consider holomorphic maps $ F $ from Levi non-degenerate real hypersurfaces $ M_{\ell} \subset \mathbb{C}^n $ to a hyperquadric $ \mathbb{H}_{\ell}^N $ with the same signature $ \ell $ and $ N - n < n - 1 $. We show that $ F $ is either CR transversal to $ \mathbb{H}_{\ell}^N $ or maps a neighborhood of $ M_{\ell} $ in $ \mathbb{C}^n $ into $ \mathbb{H}_{\ell}^N $. Furthermore, in the case where $ \ell' > \ell $, we prove that if $ F $ is not CR transversal at $0\in M_\ell$, then it must be transversally flat. This talk is based on joint work with Xiaojun Huang.
CR transversality of holomorphic maps between real hypersurfaces
11.11.2024 12:00 - 13:30
Organiser:
Luke Edholm
Location:
BZ09