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arXiv · 1508.03915

Birational contractions of $\overline{\mathrm{M}}_{0,n}$ and combinatorics of extremal assignments

Han-Bom Moon·Charles Summers·James von Albade·Ranze Xie
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Abstract

From Smyth's classification, modular compactifications of pointed smooth rational curves are indexed by combinatorial data, so-called extremal assignments. We explore their combinatorial structures and show that any extremal assignment is a finite union of atomic extremal assignments. We discuss a connection with the birational geometry of the moduli space of stable pointed curves. As applications, we study three special classes of extremal assignments: smooth, toric, and invariant with respect to the symmetric group action. We identify them with three combinatorial objects: simple intersecting families, complete multipartite graphs, and special families of integer partitions, respectively.

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Han-Bom Moon, Charles Summers, James von Albade, Ranze Xie. 2015-08-17. Birational contractions of $\overline{\mathrm{M}}_{0,n}$ and combinatorics of extremal assignments. https://arxiv.org/abs/1508.03915

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