Multivariate Hilbert Polynomials For Smooth Projective Toric Varieties
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Authors
Hersey, Benjamin S
Date
Type
thesis
Language
eng
Keyword
Mathematics
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Abstract
Generalizing Hilbert polynomials for varieties embedded in projective space, we develop the theory of multivariate Hilbert polynomials for varieties embedded in a smooth projective toric variety. These polynomials can be understood either as an Euler characteristic, or as a vector partition function. We give a characterization of toric projective bundles via local cohomology. We use this characterization to show that, for smooth projective toric surfaces, the multivariate Hilbert polynomial of the Cox ring is reducible if and only if the Picard rank of the surface is less than or equal to 2. For smooth projective toric varieties of dimension greater than 2, we investigate the connection between reducibility of the Hilbert polynomial of the Cox ring, and the splitting of the fan of the variety.
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This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.