Abstract
In this article, we give a survey of geometric invariant theory for Toric Varieties, and present an application to the Einstein–Weyl geometry. We compute the image of the Minitwistor space of the Honda metrics as a categorical quotient according to the most efficient linearization. The result is the complex weighted projective space C P 1 , 1 , 2 . We also find and classify all possible quotients.
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