arXiv subjects

Anna-Sofie Schilling

Publications and source records attributed to Anna-Sofie Schilling.

3 recordsLinked to original sources

arXiv2024

Polyhedral Horofunction Compactification as a Polyhedral Ball

In this paper we answer positively a question raised by Kapovich and Leeb in a paper titled "Finsler bordifications of symmetric and certain locally symmetric spaces". Specifically, we show that for a finite-dimensional vector space with a polyhedral norm, its horofunction compactification is homeomorphic to the dual unit ball of the norm by an explicit map. To prove this, we establish a criterion for converging sequences in the horofunction compactification and generalize the basic notion of the moment map in the theory of toric varieties.

math.GT↗

arXiv2018

Horofunction Compactifications of Symmetric Spaces

We consider horofunction compactifications of symmetric spaces with respect to invariant Finsler metrics. We show that any (generalized) Satake compactification can be realized as a horofunction compactification with respect to a polyhedral Finsler metric.

math.DG↗

arXiv2017

Toric Varieties vs. Horofunction Compactifications of Polyhedral Norms

We establish a natural and geometric 1-1 correspondence between projective toric varieties of dimension $n$ and horofunction compactifications of $\mathbb{R}^n$ with respect to rational polyhedral norms. For this purpose, we explain a topological model of toric varieties. Consequently, toric varieties in algebraic geometry, normed spaces in convex analysis, and horofunction compactifications in metric geometry are directly and explicitly related.

math.MG↗