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

Abstract

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.

7 pages, 3 figures

Cited by in corpus (3)

• Semiampleness criteria for divisors on ${\overline{M}}_{0,n}$
• Effective curves on ${\overline{M}}_{0,n}$ from group actions
• Basepoint free cycles on ${\overline{M}}_{0,n}$ from Gromov-Witten theory