A polygonal presentation of $Pic(\overline{\mathfrak{M}}_{0,n})$

Details A polygonal presentation of $Pic(\overline{\mathfrak{M}}_{0,n})$ A polygonal presentation of $Pic(\overline{\mathfrak{M}}_{0,n})$

2009-11-13

arxiv.org/abs/0911.2649v1

Mathematics

Algebraic Geometry

7 pages, 3 figures

Scientific paper

In the first section of this article, we recall Keel's well-known presentation of $Pic(\overline{\mathfrak{M}}_{0,n})$ using irreducible boundary divisors of $\overline{\mathfrak{M}}_{0,n}$ as generators, and describe a basis for $Pic(\overline{\mathfrak{M}}_{0,n})$ recently discovered by Keel and Gibney. In the second section, we present a theorem which gives an explicit and very simple expression for every boundary divisor in terms of this basis, thereby yielding a new presentation with a minimal set of relations.

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