The minimal model program is a framework in algebraic geometry aimed at classifying algebraic varieties by simplifying them to their 'minimal' forms. This approach focuses on transforming varieties through a series of operations, such as blow-ups and contractions, to obtain a simpler model that retains essential geometric properties. By working towards minimal models, this program connects deeply with the classification of algebraic surfaces and provides insights into specific types of surfaces, such as ruled and rational ones.
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