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Pants decompositions of random surfaces
Pants decompositions of random surfaces

... hyperbolic pairs of pants is easy to descibe: the boundary curves may have any positive lengths, and for each choice of lengths there is a unique metric. Now our plan consists of describing all the ways to glue together hyperbolic pairs of pants to make a closed hyperbolic surface, and then estimati ...
SIMPLEST SINGULARITY IN NON-ALGEBRAIC
SIMPLEST SINGULARITY IN NON-ALGEBRAIC

1

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.
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