Journal ArticleProjectivity of the moduli of equidimensional branchvarietiesHalpern-Leistner, Daniel [Department of Mathematics, Cornell University, Ithaca, New York, USA daniel.hl@cornell.edu]; Fernandez_Herrero, Andres [Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania, USA andresfh@sas.upenn.edu]; Jones, Trevor [Department of Mathematics, Johns Hopkins University, Baltimore, Maryland, USA ttj9@cornell.edu]; Ramkumar, Ritvik [Department of Mathematics, University of Notre Dame, South Bend, Indiana, USA rramkuma@nd.edu]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.Duke University Press2026-02-1510676107Duke Mathematical Journal17530012-7094https://doi.org/10.1215/00127094-2025-00322052936; 1945478National Science Foundation