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Full-Text Articles in Physical Sciences and Mathematics
Moduli Spaces Of Flat Gsp-Bundles, Neal David Livesay
Moduli Spaces Of Flat Gsp-Bundles, Neal David Livesay
LSU Doctoral Dissertations
A classical problem in the theory of differential equations is the classification of first-order singular differential operators up to gauge equivalence. A related algebro-geometric problem involves the construction of moduli spaces of meromorphic connections. In 2001, P. Boalch constructed well-behaved moduli spaces in the case that each of the singularities are diagonalizable. In a recent series of papers, C. Bremer and D. Sage developed a new approach to the study of the local behavior of meromorphic connections using a geometric variant of fundamental strata, a tool originally introduced by C. Bushnell for the study of p-adic representation theory. Not only …
On The Infinitesimal Theory Of Chow Groups, Benjamin F. Dribus
On The Infinitesimal Theory Of Chow Groups, Benjamin F. Dribus
LSU Doctoral Dissertations
The Chow groups of codimension-p algebraic cycles modulo rational equivalence on a smooth algebraic variety X have steadfastly resisted the efforts of algebraic geometers to fathom their structure. Except for the case p=1, which yields an algebraic group, the Chow groups remain mysterious. This thesis explores a "linearization" approach to this problem, focusing on the infinitesimal structure of the Chow groups near their identity elements. This method was adumbrated in recent work of Mark Green and Phillip Griffiths. Similar topics have been explored by Bloch, Stienstra, Hesselholt, Van der Kallen, and others. A famous formula of Bloch expresses the Chow …