Pedagogical notes on line bundles on complex projective manifolds - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T20:12:39Z http://mathoverflow.net/feeds/question/102934 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/102934/pedagogical-notes-on-line-bundles-on-complex-projective-manifolds Pedagogical notes on line bundles on complex projective manifolds aglearner 2012-07-23T15:10:04Z 2012-07-24T01:29:07Z <p>I would like to find some notes (or book), that explains on a very basic level what is a line bundle on a complex projective manifold. Maybe even, what is a line bundle on \$\mathbb CP^n\$. It seems to me that in a "usual" algebro-geometric approach line bundles come quite late, only after one defines what is a sheaf, ect. I wonder if this can be explained in "quicker" way?</p> http://mathoverflow.net/questions/102934/pedagogical-notes-on-line-bundles-on-complex-projective-manifolds/102937#102937 Answer by Francesco Polizzi for Pedagogical notes on line bundles on complex projective manifolds Francesco Polizzi 2012-07-23T15:23:38Z 2012-07-23T15:23:38Z <p>I think there are several good references. For instance:</p> <p>R. O. Wells: <em>Differential Analysis on complex manifolds</em> (Springer GTM <strong>65</strong>), Chapter III.</p> <p>J. D. Moore: <em>Lectures in Seiberg-Witten invariants</em> (Springer LNM <strong>1629</strong>), Chapter 1. </p> <p>D. Huybrechts: <em>Complex Geometry - An introduction</em> (Springer Universitext), Chapter 2.</p> http://mathoverflow.net/questions/102934/pedagogical-notes-on-line-bundles-on-complex-projective-manifolds/102949#102949 Answer by Margaret Friedland for Pedagogical notes on line bundles on complex projective manifolds Margaret Friedland 2012-07-23T17:30:29Z 2012-07-23T17:30:29Z <p>If you want complex vector bundles (or even complex fiber bundles) presented at a "very basic level" (without sheaf theory), try Chapter IV of </p> <p>Fritzsche, Klaus; Grauert, Hans: From holomorphic functions to complex manifolds. Graduate Texts in Mathematics, 213. Springer-Verlag, New York, 2002. xvi+392 pp. ISBN: 0-387-95395-7 </p> http://mathoverflow.net/questions/102934/pedagogical-notes-on-line-bundles-on-complex-projective-manifolds/102973#102973 Answer by David Corwin for Pedagogical notes on line bundles on complex projective manifolds David Corwin 2012-07-24T01:29:07Z 2012-07-24T01:29:07Z <p>For a slightly different approach, I recommend <em>Algebraic Curves and Riemann Surfaces</em> by Rick Miranda. This book starts out by developing everything in terms of divisors, then turns to line bundles and sheaves. I recommend it precisely because it works at developing lots of motivation for the notion of a sheaf (as well as that of sheaf cohomology).</p>