most recent 30 from http://mathoverflow.net 2013-05-26T01:04:38Z http://mathoverflow.net/feeds/user/14506 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/62193/what-do-poles-of-differentials-on-a-curve-mean goooooooogle 2011-04-19T04:01:29Z 2011-04-19T23:08:32Z

<p>Let C be a (smooth proper) curve. I think of an element f of the (algebraic) function field of C as, literally, a map from C to P1. Poles of f literally mean the fiber over infinty, and div f makes good sense to me.</p> <p>How should I think of a pole of a differential? I.e., let K(C) be the function field of C and define Omega(C) to be the set of symbols df for f in K(C), modulo the usual relations. Let w in Omega(C). I understand quite well the yoga of defining and manipulating div w; my question is -- how, exactly, should I think of poles of w?</p>