Moduli Space

In algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space. In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects.

Read more about Moduli Space:  Definitions, Methods For Constructing Moduli Spaces, In Physics

Famous quotes containing the word space:

    There is commonly sufficient space about us. Our horizon is never quite at our elbows.
    Henry David Thoreau (1817–1862)