Wiktionary
vb. (present participle of blow up English)
WordNet
n. a severe rebuke; "he deserved the berating that the coach gave him" [syn: berating]
Wikipedia
In mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with all the directions pointing out of that subspace. For example, the blowup of a point in a plane replaces the point with the projectivized tangent space at that point. The metaphor is that of zooming in on a photograph to enlarge part of the picture, rather than referring to an explosion.
Blowups are the most fundamental transformation in birational geometry, because every birational morphism between projective varieties is a blowup. The weak factorization theorem says that every birational map can be factored as a composition of particularly simple blowups. The Cremona group, the group of birational automorphisms of the plane, is generated by blowups.
Besides their importance in describing birational transformations, blowups are also an important way of constructing new spaces. For instance, most procedures for resolution of singularities proceed by blowing up singularities until they become smooth. A consequence of this is that blowups can be used to resolve the singularities of birational maps.
Classically, blowups were defined extrinsically, by first defining the blowup on spaces such as projective space using an explicit construction in coordinates and then defining blowups on other spaces in terms of an embedding. This is reflected in some of the terminology, such as the classical term monoidal transformation. Contemporary algebraic geometry treats blowing up as an intrinsic operation on an algebraic variety. From this perspective, a blowup is the universal (in the sense of category theory) way to turn a subvariety into a Cartier divisor.
A blowup can also be called monoidal transformation, locally quadratic transformation, dilatation, σ-process, or Hopf map.
Usage examples of "blowing up".
Aid is closely correlated with improvement in the investment climate, a result commonly achieved by murdering priests and union leaders, massacring peasants trying to organize, blowing up the independent press, and so on.
But the hazard of the kid blowing up was an unease sitting like lead at the pit of his own stomach—.
A winter wind chilled his face and torso, blowing up from unimaginable depths.
It has split the lower part of the hull, instead of blowing up the deck and topsides!
It only took Papa O'Neal blowing up one cow for her to decide she wanted to be real careful.
Some -- fool showed them the pictures of Psychlo blowing up and they just won't do anything!
It was brown and blowing in the wind and Thomas Hudson thought that with this wind blowing up they would have much less than the Mean Low Water depths.
Shaftoe has found that, for an organization devoted to shooting and blowing up people on a large scale, the military is infuriatingly reticent about passing out weapons.