Presented By: Algebraic Geometry Seminar  Department of Mathematics
Algebraic Geometry Seminar (note special day and location): Ample vector bundles and moduli of tame stacks
Rachel Webb (Cornell)
Ample line bundles on schemes have many equivalent characterizations, but one key feature is that they can be used to embed the base scheme into a projective space. I will present two natural definitions of an ample vector bundle on a stack, not clearly equivalent, one generalizing a cohomological property and the other generalizing the embedding property of ample line bundles. Using the latter, and extending work of Kresch, I will explain how an ample vector bundle on a tame stack induces an embedding into [V^s/GL_r] where V^s is the twisted affine GIT stable locus in some polynomial representation V of GL_r. An application is the construction of moduli of stacks with ample vector bundle and in particular a very general stack of tame stacky curves. This is joint with Daniel Bragg and Martin Olsson.
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