Reference for explicit calculation of blowups (of ideals) and strict transforms - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T13:50:16Z http://mathoverflow.net/feeds/question/5012 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/5012/reference-for-explicit-calculation-of-blowups-of-ideals-and-strict-transforms Reference for explicit calculation of blowups (of ideals) and strict transforms unknown (google) 2009-11-11T09:19:04Z 2010-04-19T15:30:17Z <p>Can one suggest some references where explicit calculations for blow up technique(along an ideal) and strict transformation is done in different examples?</p> http://mathoverflow.net/questions/5012/reference-for-explicit-calculation-of-blowups-of-ideals-and-strict-transforms/5021#5021 Answer by David Lehavi for Reference for explicit calculation of blowups (of ideals) and strict transforms David Lehavi 2009-11-11T10:07:35Z 2009-11-11T10:07:35Z <p>Both Hartshorne and Fulton's Intersection theory contain many examples. Look for the terms "Blow up" and "Monoidal transform". There are also some "hands on" examples in Dolgachev's <a href="http://www.math.lsa.umich.edu/~idolga/topics1.pdf" rel="nofollow">classical algebraic geometry online book</a> . The standard example is describing a cubic surface as a plane with 6 blown up points; see Hartshorne V.4 </p> http://mathoverflow.net/questions/5012/reference-for-explicit-calculation-of-blowups-of-ideals-and-strict-transforms/5657#5657 Answer by Shom for Reference for explicit calculation of blowups (of ideals) and strict transforms Shom 2009-11-15T23:55:23Z 2009-11-15T23:55:23Z <p>I suggest Beauville's Complex Algebraic Surfaces.</p> http://mathoverflow.net/questions/5012/reference-for-explicit-calculation-of-blowups-of-ideals-and-strict-transforms/21041#21041 Answer by Csar Lozano Huerta for Reference for explicit calculation of blowups (of ideals) and strict transforms Csar Lozano Huerta 2010-04-11T21:44:32Z 2010-04-11T21:44:32Z <p>I think, you'd like to see explicit equations and if possible, a singularity completely solved by blowups. One can take a look at such thinks in <strong>Lectures on resolution of singularities</strong> by Janos Kollar (http://press.princeton.edu/titles/8449.html). The book starts with more than ten different methods of how to solve singularities on curves and then continues on resolution of singularities on surfaces. There you will see specific examples and explicit equations.</p> http://mathoverflow.net/questions/5012/reference-for-explicit-calculation-of-blowups-of-ideals-and-strict-transforms/21843#21843 Answer by J.C. Ottem for Reference for explicit calculation of blowups (of ideals) and strict transforms J.C. Ottem 2010-04-19T14:55:03Z 2010-04-19T14:55:03Z <p>There are several explicit calculations given in Chapter IV.2 of Eisenbud and Harris' <a href="http://books.google.no/books?id=FjtDugVYMIMC&amp;pg=PA162&amp;lpg=PP1&amp;dq=geometry+of+schemes#v=onepage&amp;q&amp;f=false" rel="nofollow">Geometry of Schemes</a></p> http://mathoverflow.net/questions/5012/reference-for-explicit-calculation-of-blowups-of-ideals-and-strict-transforms/21844#21844 Answer by Daisy for Reference for explicit calculation of blowups (of ideals) and strict transforms Daisy 2010-04-19T15:30:17Z 2010-04-19T15:30:17Z <p>You can try out Hauser's seven short stories (with lots of examples and exercises!) <a href="http://homepage.univie.ac.at/herwig.hauser/Publications/seven%20short%20stories%20on%20blowups%20and%20resolution/seven%20short%20stories%20on%20blowups%20and%20resolution.pdf" rel="nofollow">http://homepage.univie.ac.at/herwig.hauser/Publications/seven%20short%20stories%20on%20blowups%20and%20resolution/seven%20short%20stories%20on%20blowups%20and%20resolution.pdf</a> some more examples are in <a href="http://homepage.univie.ac.at/herwig.hauser/Publications/seventeen-obstacles-97.pdf" rel="nofollow">http://homepage.univie.ac.at/herwig.hauser/Publications/seventeen-obstacles-97.pdf</a></p>