English

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

R2 v1 2026-06-23T00:23:53.307Z