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Exploration of vector bundles with positive Chern class in complex projective varieties, suggesting new examples.
A class of vector bundles of rank on an ‐dimensional complex projective variety , spanned by global sections, with positive top Chern class and ample determinant is investigated. The standard relation between Chern and Segre polynomials allows us to decide about the bigness of a bundle closely related to . The size , an integer measuring the deviation of from bigness, is introduced and studied. The structure of , in connection with the behavior of the size, yields a useful tool to produce several examples. Among them the pair emerges, of which two characterizations are provided in terms of and in terms of the degree of curves representing with respect to the determinant.
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Lanteri et al. (2026) studied this question.
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