Welcome to MathOverflow

Question

0

1

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 $I_O(f,g)>de.$

edited Apr 25 at 7:05

asked Oct 12 2011 at 2:52

mfn
11●2

5

mfn -- 1. what is the question? 2. there is a much better chance of getting a good answer if you make the question easier to read (hint: dollars). – algori Oct 12 2011 at 3:51

7

@algori: the dollar hint makes you sound like you're asking for a bribe. Of course, if you'd asked for latex instead, who knows what it would make it sound like... – Thierry Zell Oct 12 2011 at 12:11

ulrich · Answer 1 · 2011-10-12 11:03:56Z UTC

3

This is proved in Fulton's "Algebraic Curves", available online here. The precise reference is Section 3.3, property (5) on p. 37.

answered Oct 12 2011 at 11:03

ulrich
6,785●1●14●23

Intersection of curves

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

1 Answer

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.