Singular Curve Problem from Hartshorne, Exercise IV.1.8.C - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-26T08:13:42Z http://mathoverflow.net/feeds/question/106289 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/106289/singular-curve-problem-from-hartshorne-exercise-iv-1-8-c Singular Curve Problem from Hartshorne, Exercise IV.1.8.C Omprokash Das 2012-09-04T00:48:08Z 2012-09-04T00:48:08Z <p>Let $X$ be an integral projective scheme of dimension $1$ over $k$, where $k$ is an algebraically closed field, and let $\tilde{X}$ be its normalization. Let $\delta_P$=length$(\tilde{\mathcal{O}_P}/\mathcal{O}_P)$ where $P\in X$. </p> <p>Show that $\delta_P$ depends only on the analytic isomorphism class of the singularity at $P$.</p>