I'm looking at the variety $\mathbb{V}(xy) \subseteq \mathbb{A}^2$, and I'm trying to calculate $\mathcal{O}_{X,p}$ where $p = (0,0)$.
I was wondering if there is a nice way to calculate this?
I've got that functions can be written as $$ \frac{f_1(x) + yg_1(y)}{f_2(x) + yg_2(y)} $$ uniquely, then got some relations on the $f_i$ and $g_i$ if two functions agree on some open set containing the origin, but can't seem to describe the stalk nicely.
Thanks for any help.