Stable maps

Stable maps are mathematical tools used in geometry to study how shapes called "curves" can be smoothly mapped onto other surfaces or spaces. They help mathematicians understand how these curves can change, deform, or connect within complex shapes, especially when some parts might collapse or become singular. The "stability" condition ensures these maps remain well-behaved and manageable, even when the curves develop certain degenerations. Essentially, stable maps provide a structured way to track and classify how curves fit into larger geometric frameworks, supporting advanced research in areas like algebraic geometry and string theory.