Log Canonical Threshold

The log canonical threshold (LCT) is a mathematical measure that quantifies the complexity or severity of singularities (points where a shape or space is "not smooth") in a geometric object, such as a variety or a divisor. It indicates how much you can "scale" or "perturb" the object before its singularities become too complicated to handle within certain technical frameworks. A higher LCT means milder singularities, while a lower LCT signals more severe issues. This concept helps mathematicians understand and classify singularities, playing a key role in areas like algebraic geometry and the study of complex spaces.