Virtual Cartier divisors and blow-ups
Algebraic Geometry
2025-11-14 v2
Abstract
We prove a universal property for blow-ups in regularly immersed subschemes, based on a notion we call "virtual effective Cartier divisor". We also construct blow-ups of quasi-smooth closed immersions in derived algebraic geometry.
Keywords
Cite
@article{arxiv.1802.05702,
title = {Virtual Cartier divisors and blow-ups},
author = {Adeel A. Khan and David Rydh},
journal= {arXiv preprint arXiv:1802.05702},
year = {2025}
}
Comments
19 pages; version 2 adds a comparison between virtual and generalized Cartier divisors, a new section on simultaneous blow-ups in multiple centres and blow-ups in unramified centres, and a new co-author