Examples of varieties of structures

Details Examples of varieties of structures Examples of varieties of structures

2012-02-24

arxiv.org/abs/1202.5530v1

Mathematics

Algebraic Geometry

Scientific paper

In this article we will introduce, among others, the variety of subcomplexes and the variety of maps between complexes of given rank. Also, varieties of $\mathfrak{g}$-structure like $\mathfrak{g}$-Grassmannian, $\mathfrak{g}$-determinantal varieties and finally the variety $\mathcal{DGLA}(E)$ of differential graded Lie algebra structures on $E$. We will compute the dimensions of these varieties and also some relevant properties. The motivation of this article is to give examples of moduli spaces relevant to deformation theory.

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