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单词 Moduli space
释义

Moduli space

中文百科

模空间

在代数几何上,模问题用于描述代数簇所依赖的参数。对于这样一个参数使用模这一词和模形式相似:一个模形式通常是模空间(也即,其坐标为模的空间)上的某种微分形式(或者张量密度),因为这些形式通常有一个权重)。

在椭圆曲线的情况,有一个模,所以模空间是代数曲线。这是在雅可比的椭圆函数理论中称为k的一个量,他将椭圆积分归约为如下形式

\sqrt{(1-x^2)(1-k^2x^2)\,}.
英语百科

Mo**** space 模空间

Constructing P1(R) by varying 0 ≤ θ < π or as a quotient space of S1.

In algebraic geometry, a mo**** 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"; mo**** spaces were first understood as spaces of parameters rather than as spaces of objects.

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更新时间:2025/6/23 15:15:07