Bounding toric singularities with normalized volume
Joaquín Moraga,
Hendrik Süß
Abstract:We study the normalized volume of toric singularities. As it turns out, there is a close relation to the notion of (nonsymmetric) Mahler volume from convex geometry. This observation allows us to use standard tools from convex geometry, such as the Blaschke–Santaló inequality and Radon's theorem to prove nontrivial facts about the normalized volume in the toric setting. For example, we prove that for every there are only finitely many ‐Gorenstein toric singularities with normalized volume at least . From this… Show more
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