limits of algebraic varieties - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T03:37:23Z http://mathoverflow.net/feeds/question/3232 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/3232/limits-of-algebraic-varieties limits of algebraic varieties Thomas Sauvaget 2009-10-29T09:02:01Z 2009-10-29T10:13:30Z <p>I'm looking for a reference which deals with limits of families of algebraic varieties as the degree increases (or at least keywords from this subject). </p> <p>For the kind of example I have in mind, consider the exponential function as a convergent power series e^x=1+x+x^2/2!+... on the interval [-1;1] say, and consider the varieties A0:={(x,y)\in\R^2 s.t. y=1}, A1:={(x,y)\in\R^2 s.t. y=1+x}, A2:={(x,y)\in\R^2 s.t. y=1+x+x^2/2!}... which converge (in the euclidean topology) to the graph of the exponential (as in the picture <a href="http://en.wikipedia.org/wiki/Exponential%5Ffunction#Formal%5Fdefinition" rel="nofollow">here</a>). </p> http://mathoverflow.net/questions/3232/limits-of-algebraic-varieties/3238#3238 Answer by lhf for limits of algebraic varieties lhf 2009-10-29T10:13:30Z 2009-10-29T10:13:30Z <p>See <a href="http://www.tecgraf.puc-rio.br/~lhf/ftp/doc/limits.pdf" rel="nofollow">On the limit of families of algebraic subvarieties with unbounded volume</a>, to appear in Astérisque.</p>