Smooth blow up structures on projective bundles
Algebraic Geometry
2024-12-03 v1
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.
Cite
@article{arxiv.2412.00021,
title = {Smooth blow up structures on projective bundles},
author = {Supravat Sarkar},
journal= {arXiv preprint arXiv:2412.00021},
year = {2024}
}