Slicing up multigraded linear series
arXiv:2306.12750
Abstract
Multigraded linear series generalize the classical morphism to the linear series of a basepoint-free line bundle on a scheme. We investigate the collection of the natural cornering morphisms into elementary bigraded linear series obtained from direct summands of the original globally generated vector bundle. Our main result is a condition on the injectivity of the product morphism. We apply our result in two examples: modules over the reconstruction algebra and equivariant Hilbert and Quot schemes of quotient stacks.
12 pages, final version