Conditions for semistable vector bundles with specific holomorphic sections are established, suggesting effective strategies in geometry.
On an arbitrary compact Riemann surface, necessary and suflicient conditions are found for the existence of semistable vector bundles with slope between zero and one and a prescribed number of linearly independent holomorphic sections. Existence is achieved by minimizing the Yang-Mills-Higgs functional.
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Daskalopoulos et al. (1999) studied this question.
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