Blow-ups

I am an analyst and though I do appreciate algebraic geometry, my knowledge is rather limited. However, recently I have been in need to understand blow-ups in manifolds with corners (^[1]).

By doing so, I felt the need to understand these blow-ups a bit bettter even from the algebraic point of view and have been searching for good introductory ressources. In particular it it seemed to be a good time to get some loose grip on Hironaka's result. Following the title of Herwig Hauser's article "The proof I always wanted to understand."

Here are some links to wokrs that I found helpful:

Introductory

• Hauser, 2000: Resolution of singularities 1860-1999 in Resolution of Singularities (with H.Hauser, J.Lipman, F.Oort, A.Quirós), Educational Progress in Math. 181, Birkhäuser (2000)
• Hauser, 2003. The Hironaka Theorem on Resolution of Singularities in Bull. Amer. Math. Soc. 40 (2003), 323-403.
• Hauser, 2005: Seven short stories on blowups and resolution in Proceedings of the 12th Converence. Published on gokovagt.org.
• Hauser, 2014: Blowups and Resolutions in The resolution of singular algebraic varieties, Clay Mathematics Institute Summer School 2012, Obergurgl. CMI series, Amer. Math. Soc. 2014, pp. 1-80. arXiv
• Spivakovsky, 2020: Resolution of Singularities: An Introduction in Handbook of Geometry and Topology of Singularities I, ISBN 978-3-030-53060-0 . DOI
• Nunez Lopez-Benito, 2017: Blowups in Algebraic Geometry in Bachelor Thesis at the Ludwig-Maximilians-Universität München under supervision of Nikita Semenov.

Videos

• Borcherds, 2021: Online Course on Algebraic Geometry (In particular lecture 34,35 in AGI and 45 in AGII.)
  • YouTube playlist Algebraic geometry I: Varieties
  • YouTube playlist Algebraic geometry II: Schemes