2024/11/16 by Supravat Sarkar, Sarkar, Supravat
Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Algebraic Geometry (math.AG) #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2412.00021
openalex publication_date 2024/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.