Minimal Model Program

The Minimal Model Program (MMP) is a strategy in algebraic geometry that aims to simplify complex geometric shapes called varieties, which are higher-dimensional analogs of surfaces. By performing specific transformations, such as contractions and flips, the MMP systematically reduces these shapes to simpler forms called minimal models or Mori fiber spaces, while preserving their essential properties. This process helps mathematicians classify and understand the structure of these varieties, just as simplifying a complicated object reveals its core features. Overall, the MMP provides a structured approach to organizing and analyzing the diversity of algebraic shapes.