On the Calabi composition of multiple affine hyperspheres
Li Xingxiao
TL;DR
This paper explicitly constructs the Calabi composition of multiple affine hyperspheres, including points, and analyzes their affine invariants, establishing conditions for symmetry based on the factors.
Contribution
It provides an explicit construction method for the Calabi composition of affine hyperspheres and characterizes when the composition remains symmetric.
Findings
The composition includes points as 0-dimensional hyperspheres.
All basic affine invariants of the composition are computed.
The composition is symmetric if and only if each positive-dimensional factor is symmetric.
Abstract
In this paper, we explicitly construct the Calabi composition of multiple affine hyperspheres possibly including some points viewing as 0-dimensional hypersheres. Then we compute all the basic affine invariants of the composed affine hyperspheres, proving that the composed affine hypersphere is symmetric one if and only if each of its composing factors of positive dimension is symmetric.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Advanced Topics in Algebra · Advanced Combinatorial Mathematics