Level Structure

(Algebraic Geometry)

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Algebraic Geometry
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What is Level structure (algebraic geometry)?

In algebraic geometry, a level structure on a space X is an extra structure attached to X that shrinks or eliminates the automorphism group of X, by demanding automorphisms to preserve the level structure; attaching a level structure is often phrased as rigidifying the geometry of X. In applications, a level structure is used in the construction of moduli spaces; a moduli space is often constructed as a quotient. The presence of automorphisms poses a difficulty to forming a quotient; thus introducing level structures helps overcome this difficulty. There is no single definition of a level structure; rather, depending on the space X, one introduces the notion of a level structure. The classic one is that on an elliptic curve (see ). There is a level structure attached to a formal group called a Drinfeld level structure, introduced in .

Technology Types

algebraic geometry

Synonyms

Rigidify

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