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Seminar
FIELD Mathematics
DATE April 19 (Thu), 2018
TIME 14:00-15:30
PLACE 1423
SPEAKER Kwok Kin Wong
HOST Hwang, Jun-Muk
INSTITUTE KIAS
TITLE Zariski closures of images of algebraic subsets under uniformization map of complex unit balls
ABSTRACT

Let $S$ be an irreducible algebraic subset of the complex unit ball $\mathbb{B}^n$ and $\pi: \mathbb{B}^n\rightarrow X_\Gamma= \mathbb{B}^n/\Gamma$ is the universal covering map to a quotient by irreducible torsion free lattice. We show by complex differential geometric techniques that the Zariski closure $Z=\overline{\pi(S)}^{Zar}$ in $X_\Gamma$ is a totally geodesic subset. It is an analogue of the hyperbolic Ax-Lindemann-Weierstrass conjecture in rank $1$ case, especially where the arithmeticity is unnecessary.

The result is the main theorem of a recent preprint of Mok: http://hkumath.hku.hk/~imr/IMRPreprintSeries/2017/IMR2017-2.pdf.

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