Intersection of curves - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T20:25:00Z http://mathoverflow.net/feeds/question/77887 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/77887/intersection-of-curves Intersection of curves mfn 2011-10-12T02:52:07Z 2013-04-25T07:05:22Z <p>Let $f(x,y)=0$ and $g(x,y)=0$ be curves in $\mathbb R^2$. Assume that the origin $(0,0)\in \mathbb R^2$ is a $d$-fold point of $f$ and an $e$-fold point of $g$, respectively. Let $f_d(x,y)$ be the sum of the terms of degree $d$ in $f(x,y)$, $g_e(x,y)$ be the sum of the terms of degree $e$ in $g(x,y)$. If $f_d(x,y)$ and $g_e(x,y)$ have a common factor of positive degree, then the intersection multiplicity $I_O(f,g)>de.$</p> http://mathoverflow.net/questions/77887/intersection-of-curves/77914#77914 Answer by ulrich for Intersection of curves ulrich 2011-10-12T11:03:56Z 2011-10-12T11:03:56Z <p>This is proved in Fulton's "Algebraic Curves", available online <a href="http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf" rel="nofollow">here</a>. The precise reference is Section 3.3, property (5) on p. 37.</p>