Título: | The Arithmetic of Simple Singularities |
Autores: | Thorne, Jack A. |
Fecha: |
2012-08-10 2012-08-10 2012 2012-08-10 |
Publicador: | |
Fuente: |
Ver documento Ver documento |
Tipo: | Thesis or Dissertation |
Tema: | mathematics |
Descripción: |
We investigate some arithmetic orbit problems in representations of linear algebraic groups arising from Vinberg theory. We aim to give a description of the orbits in these representations using methods with an emphasis on representation theory rather than algebraic geometry, in contrast to previous works of other authors. It turns out that for the representations we consider, the orbits are related to the arithmetic of the Jacobians of certain algebraic curves, which appear as the smooth nearby fibers of deformations of simple singularities. We calculate these families of algebraic curves, and show that the 2-torsion in their Jacobians is canonically identified with the stabilizers of certain orbits in the corresponding representations. Mathematics |
Idioma: | Inglés |
1 Direct parsing of ID/LP grammars por Shieber, Stuart | 6 Semantic-head-driven generation por Moore, Robert C.,Pereira, Fernando C. N.,van Noord, Gertjan,Shieber, Stuart |
2 Synchronous grammars as tree transducers por Shieber, Stuart | 7 Ellipsis and higher-order unification por Pereira, Fernando C. N.,Dalrymple, Mary,Shieber, Stuart |
3 Automatic yellow-pages pagination and layout por Marks, Joe,Shieber, Stuart,Johari, Ramesh,Partovi, Ali | 8 Generation and synchronous tree-adjoining grammars por Shieber, Stuart,Schabes, Yves |
4 Evidence against the context-freeness of natural language por Shieber, Stuart | 9 The Research Library in the Digital Age por Darnton, Robert |
5 An algorithm for generating quantifier scopings por Hobbs, Jerry,Shieber, Stuart | 10 The Turing test as interactive proof por Shieber, Stuart |