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| Author(s): |
Miriam da Silva Pereira
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2010-04-29 |
| Examining board members: |
Maria Aparecida Soares Ruas;
Lev Birbrair;
Jean Paul Brasselet;
Washington Luiz Marar;
João Nivaldo Tomazella
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| Advisor: | Maria Aparecida Soares Ruas |
| Abstract | |
The theorem of Hilbert- Burch provides a good description of codimension two determinantal varieties and their deformations in terms of their presentation matrices. In this work we use this correspondence to study properties of determinantal varieties, based on methods of singularity theory of their presentation matrices. In the first part of the thesis we establish the theory of singularities for n X p matrices extending previous results of J. W. Bruce and F. Tari in [5], for classes of square matrices, and A. Frühbis-Krüger for n X (n+1) matrices in [16]. In the second part we concentrate on codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their generic fiber. For surfaces in \'C POT. 4\' , we obtain a Lê-Greuel formula expressing the Milnor number of the surface in terms of the second polar multiplicity and the Milnor number of the generic section (AU) | |