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

TL;DR
This paper provides a new, simplified polygonal presentation of the Picard group of the moduli space of stable n-pointed rational curves, improving understanding of its structure with minimal relations.
Contribution
It introduces an explicit, simple expression for boundary divisors in terms of a known basis, offering a minimal relation presentation of the Picard group.
Findings
Explicit formula for boundary divisors in terms of a basis
New minimal relation presentation of Picard group
Simplified polygonal representation of the moduli space
Abstract
In the first section of this article, we recall Keel's well-known presentation of using irreducible boundary divisors of as generators, and describe a basis for 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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Finite Group Theory Research · Polynomial and algebraic computation
