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arXiv · 2412.00021

Smooth blow up structures on projective bundles

Supravat Sarkar
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Abstract

Assuming Hartshorne's conjecture on complete intersections, we classify projective bundles over projective spaces which has a smooth blow up structure over another projective space. Under some assumptions, we also classify projective bundles over projective spaces which has a smooth blow up structure over some arbitrary smooth projective variety, not necessarily a projective space. We verify which of the globally generated vector bundles over projective space of first Chern class at most five has the property that their projectivisation has a smooth blow up structure, with no additional assumption. In the way, we get some new examples of varieties with both projective bundle and smooth blow up structures.

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Supravat Sarkar. 2024-11-16. Smooth blow up structures on projective bundles. https://arxiv.org/abs/2412.00021

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