On the birational geometry of spaces of complete forms II: skew-forms

TL;DR

This paper investigates the birational geometry of moduli spaces of complete skew-forms, computing their cones, Cox rings, and chamber decompositions, especially for spaces with low Picard rank.

Contribution

It provides explicit descriptions of the effective, nef, and movable cones, Cox ring generators, and chamber decompositions for these moduli spaces, advancing understanding of their birational properties.

Findings

Computed effective, nef, and movable cones.

Determined generators of Cox rings.

Described Mori chamber and base locus decompositions.

Abstract

Moduli spaces of complete skew-forms are compactifications of spaces of skew-symmetric linear maps of maximal rank on a fixed vector space, where the added boundary divisor is simple normal crossing. In this paper we compute their effective, nef and movable cones, the generators of their Cox rings, and for those spaces having Picard rank two we give an explicit presentation of the Cox ring. Furthermore, we give a complete description of both the Mori chamber and stable base locus decompositions of the effective cone of some spaces of complete skew-forms having Picard rank at most four.