Projectivity of the moduli of equidimensional branchvarieties

Abstract

We resolve an open problem posed by Alexeev-Knutson on the projectivity of the moduli of branchvarieties in the equidimensional case. As an application, we construct projective moduli spaces of reduced equidimensional varieties equipped with ample linear series and subject to a semistability condition.

34 pages. Final accepted version