# Blown up

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## Possible Answers: INFLATED.

Last seen on: NY Times Crossword 18 Dec 19, Wednesday

### Random information on the term “Blown up”:

In algebraic geometry, an infinitely near point of an algebraic surface S is a point on a surface obtained from S by repeatedly blowing up points. Infinitely near points of algebraic surfaces were introduced by Max Noether (1876).

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There are some other meanings of “infinitely near point”. Infinitely near points can also be defined for higher-dimensional varieties: there are several inequivalent ways to do this, depending on what one is allowed to blow up. Weil gave a definition of infinitely near points of smooth varieties, though these are not the same as infinitely near points in algebraic geometry.In the line of hyperreal numbers, an extension of the real number line, two points are called infinitely near if their difference is infinitesimal.

When blowing up is applied to a point P on a surface S, the new surface S* contains a whole curve C where P used to be. The points of C have the geometric interpretation as the tangent directions at P to S. They can be called infinitely near to P as way of visualizing them on S, rather than S*. More generally this construction can be iterated by blowing up a point on the new curve C, and so on.

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