The Kodaira Vanishing Theorem states that for a smooth projective variety over a field, the higher cohomology groups of certain line bundles vanish under specific conditions. This result is crucial in algebraic geometry as it establishes important connections between the geometry of a variety and its cohomological properties, leading to various applications in the study of complex manifolds and algebraic varieties.
congrats on reading the definition of Kodaira Vanishing Theorem. now let's actually learn it.