1
$\begingroup$

I am starting to study for my Msc dissertation and i want / have to study the Blowing up transformation in algebraic geometry. I know little about algebraic geometry but i'm a stubborn learner and so i can make it in the end. I would like to know some good references / books so to understand it intuitively and then more strictly.

Thank you in advance.

Improve this question
$\endgroup$
1
  • 3
    $\begingroup$ Section IV.2 of Eisenbud-Harris "Geometry of Schemes" is about blowing up. I was one of the proofreaders for that section :) $\endgroup$
    – Jason Starr
    Commented Aug 8, 2015 at 12:38

1 Answer 1

Reset to default
2
$\begingroup$

An elementary and extremely detailed account of this is given in the book Brieskorn, Knörrer: Plane Algebraic Curves.

Improve this answer
$\endgroup$
5
  • $\begingroup$ Thank you for answering, but could you please indicate me the pages because i cannot find it in the index and the book is big enough. $\endgroup$
    – Mitsos
    Commented Aug 8, 2015 at 10:21
  • $\begingroup$ @Mitsos I do not have the book with me now, but I recall that there are about 200 pages on the topic. $\endgroup$
    – Martin Peters
    Commented Aug 8, 2015 at 14:12
  • $\begingroup$ The topic is called "quadratic transformation" in the table of contents, but the term "blowing up a point" does occur in my index as on p. 462. $\endgroup$
    – roy smith
    Commented Aug 11, 2015 at 15:18
  • 1
    $\begingroup$ The discussion in Brieskorn may be only for plane curves. There is a nice discussion also in Shafarevich's Basic Algebraic Geometry, 1974, in both two and higher dimensions, in sections II.4, IV.3, and VI.2, where he uses blowups (sigma processes) to analyze birational maps of surfaces, and to construct a non projective 3 dimensional variety. $\endgroup$
    – roy smith
    Commented Aug 11, 2015 at 18:06
  • $\begingroup$ Mumford also gives a precise but intuitive description related to projecting subvarieties of projective space, on p.74 of Alg. Geom. I: Proj. varieties. $\endgroup$
    – roy smith
    Commented Aug 11, 2015 at 18:17

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .