Seminar on complex geometry (複幾何演講)

演講者：吳侊儒（中央大學數學系）
講  題：Uniform RC-positivity of direct image bundles
時  間：2026年3月9日 (星期一) 10:30-11:30
地  點：臺灣大學天數館202室
摘  要：The concept of RC-positivity and uniform RC-positivity is introduced by Xiaokui Yang to solve a conjecture of Yau on projectivity and rational connectedness of a compact K\"ahler manifold with positive holomorphic sectional curvature.
Some main theorems in Yang's proof hold under a weaker condition called weak RC-positivity.
It is therefore natural to ask if (uniform) weak RC-positivity implies (uniform) RC-positivity.
In this talk, we show that if a vector bundle $E$ is uniformly weakly RC-positive, then $E$ is RC-positive and $S^kE$ is uniformly RC-positive for $k$ large.

Organizer：Chin-Yu Hsiao