éclatement

Éclatement is a French noun meaning the act of bursting or breaking apart. It covers both literal ruptures—such as the rupture of a balloon, a container, or a membrane—and more figurative uses, including sudden, wide-scale dispersal, fragmentation, or eruption of phenomena. The term derives from éclater, to burst, and is used across disciplines to indicate a rupturing or division into components.

In mathematics, éclatement refers to the process known in English as blowing up a point on a geometric space. The operation replaces a point by an entire projective space of tangents, creating a new space with a modified structure used to study singularities, resolutions, and intersection theory. The concept is local and a standard tool in algebraic geometry and complex geometry.

In urban planning and geography, l’éclatement urbain describes the diffusion and fragmentation of urban areas into suburban and peri-urban zones. It is associated with dispersed development, rising car dependence, and challenges to central-city cohesion, planning, and service provision.

In biology and medicine, éclatement can denote cellular or vesicular rupture, such as cell lysis, or the bursting of pathological vesicles. In materials science and physics, it also describes the catastrophic failure or fragmentation of materials under stress or pressure, including explosions or the shattering of shells or containers.