Anderson, Reginald Cyril Wallis2023-03-312023-03-312023https://hdl.handle.net/2097/42947Beilinson’s resolution of the diagonal for complex projective spaces gives a locally free resolution of the structure sheaf of the diagonal as a Koszul complex, which gives a Fourier-Mukai transform inducing the identity on objects in the derived category of coherent sheaves of P[superscript n]. Since P[superscript n] is a toric variety, we can ask for a resolution of the diagonal of an arbitrary toric variety. While resolutions of the diagonal are known for toric varieties which are unimodular in the sense of Bayer-Popescu-Sturmfels, in order to generalize a resolution of the diagonal for simplicial toric varieties, we must consider smooth Deligne-Mumford toric stacks associated to a given simplicial toric variety. Here, the diagonal can fail to be a closed substack because of non-zero stabilizers at the origin, so that a direct generalization of Beilinson’s resolution will not work. ... See PDF file for full abstract.en-US© the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).http://rightsstatements.org/vocab/InC/1.0/Algebraic geometryDerived categoriesToric varietiesDissertation