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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 208: Seminar in Algebraic Geometry
Dr. Trevor Jones
UC San Diego
Projectivity of the Moduli Space of Equidimensional Branchvarieties
Abstract:
A branchvariety of a projective k-scheme X is a geometrically reduced scheme Y equipped with a finite map to X. Alexeev and Knutson showed the existence of a proper moduli space of branchvarieties with fixed Hilbert polynomial and degree sequence, but the projectivity of this space remained an open question. In this talk, we will discuss positivity results for some line bundles related to the determinant line bundle on the moduli space of equidimensional branchvarieties. As a consequence, we establish that this moduli space is projective.
Host: Dragos Oprea
October 23, 2026
4:00 PM
APM 7321
Research Areas
Algebraic Geometry****************************
