Kodaira dimension is a fundamental invariant in algebraic geometry that measures the growth rate of the space of global sections of the powers of a line bundle on a projective variety. It helps classify projective varieties by providing insights into their geometry and behavior, specifically how the number of independent global sections behaves with respect to increasing degrees. This notion is vital in distinguishing between varieties with different geometric properties and plays an essential role in the classification of algebraic surfaces and the application of Kodaira vanishing theorem.
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