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Abstract
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The aim of
this talk is to extend some existing results in the Brill-Noether theory of vector bundles
to the Brill-Noether theory of vector bundles with a fixed determinant. In order to do so we analyze a component in the Brill-Noether schemes of vector bundles with a fixed determinant. As a consequence we obtain a bound for dimension of these schemes when the determinant is the canonical line bundle and the bundles have at least $k$ number of linearly independent global sections, where $k$ is an odd natural number.
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