Back to Algebraic Geometry Seminar: Spring 2025
Algebraic Geometry Seminar
Date: Tuesday, Apr 22, 2025
Time: 3:30PM - 4:30PM
Location: LCB 225
Trevor Jones
Cornell
Title |
Projectivity of the Moduli Space of Equidimensional Branch varieties |
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. |
Algebraic Geometry