Birational contractions of M¯0,n and combinatorics of extremal assignments

From Smyth’s classification, modular compactifications of the moduli space of pointed smooth rational curves are indexed by combinatorial data, the so-called extremal assignments. We explore their combinatorial structures and show that any extremal assignment is a finite union of atomic extremal ass...

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Bibliographic Details
Published inJournal of algebraic combinatorics Vol. 47; no. 1; pp. 51 - 90
Main Authors Moon, Han-Bom, Summers, Charles, von Albade, James, Xie, Ranze
Format Journal Article
LanguageEnglish
Published New York Springer US 2018
Springer Nature B.V
Subjects
Combinatorial analysis
Combinatorics
Computer Science
Convex and Discrete Geometry
Curves
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Rational curves
Regular contraction
Birational geometry
Extremal assignment
Moduli space
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Summary:From Smyth’s classification, modular compactifications of the moduli space of pointed smooth rational curves are indexed by combinatorial data, the 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 rational 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.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-017-0769-z