Algebraic Geometry Seminar
Jun-Muk Hwang
Korea Institute for Advanced Study (KIAS)
Cartan-Fubini type extension of holomorphic maps preserving webs of rational curves
Abstract: Let $X_1$ and $X_2$ with $\mathrm{dim} X_1 = \mathrm{dim} X_2$ be two projective manifolds of Picard number 1 in projective space.
Assume that both $X_1$ and $X_2$ are covered by lines. Let $\varphi: U_1 \to U_2$ be a biholomorphic map between two connected Euclidean
open subsets $U_1 \subset X_1$ and $U_2 \subset X_2$. Suppose that both $\varphi$ and $\varphi^{-1}$ send pieces of lines to pieces of lines.
We show that $\varphi$ can be extended to a biregular morphism $\Phi: X_1 \to X_2$. This was proved by Hwang-Mok in 2001
when the indices of $X_1$ and $X_2$ are bigger than 2 and the new result is when the indices are 2. In this case, the covering family
of lines form webs of rational curves. We exploit the monodromy of the webs of lines to extend the holomorphic map.
Tuesday October 21, 2014 at 4:00 PM in SEO 636