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Explore the existence of rational curves in compact Kaehler manifolds through this 44-minute algebraic geometry lecture by Wenhao Ou from BIMSA. Examine the classic problem of studying rational curves in complex geometry, beginning with Mori's groundbreaking 1979 criterion for their existence in complex projective manifolds and its connection to Minimal Model Programs theory. Understand the limitations of Mori's algebraic methods when applied to more general complex manifolds, particularly compact Kaehler manifolds, and discover recent advances that characterize uniruled compact Kaehler manifolds. Learn how these new results extend Mori's fundamental theorem beyond projective manifolds to the broader class of compact Kaehler manifolds, providing new tools for finding rational curves in complex geometric settings where traditional algebraic methods fall short.
