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Factorization of point configurations, cyclic covers, and conformal blocks

Michele Bolognesi; Noah Giansiracusa — 2015

Journal of the European Mathematical Society

We describe a relation between the invariants of $n$ ordered points in projective $d$ -space and of points contained in a union of two linear subspaces. This yields an attaching map for GIT quotients parameterizing point configurations in these spaces, and we show that it respects the Segre product of the natural GIT polarizations. Associated to a configuration supported on a rational normal curve is a cyclic cover, and we show that if the branch points are weighted by the GIT linearization and the rational...

The universal tropicalization and the Berkovich analytification

Jeffrey Giansiracusa; Noah Giansiracusa — 2022

Kybernetika

Given an integral scheme $X$ over a non-archimedean valued field $k$ , we construct a universal closed embedding of $X$ into a $k$ -scheme equipped with a model over the field with one element $𝔽_{1}$ (a generalization of a toric variety). An embedding into such an ambient space determines a tropicalization of $X$ by previous work of the authors, and we show that the set-theoretic tropicalization of $X$ with respect to this universal embedding is the Berkovich analytification $X^{an}$ . Moreover, using the scheme-theoretic...

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