# Calculating intermediate extension on the stack of coherent sheaves of rank $1$

Let $$L$$ be a line bundle of degree $$d$$ on a curve $$X$$ and let $$x$$ be a point of $$X$$. I want to describe the intermediate extension of the constant sheaf from the stack of line bundles of degree $$d$$ to the point given by the coherent sheaf $$L(-x) \oplus O_x$$ of rank $$1$$ and degree $$d$$ with determinant $$L$$. In order to do this, can I simply calculate the intermediate extension of the constant sheaf from $$Ext^1(O_x, L(-x)) \setminus \{0\}$$ to the vector space $$Ext^1(O_x, L(-x))$$? I.e. does $$Ext^1(O_x, L(-x))$$ form an atlas for the neighborhood of the point $$L(-x) \oplus O_x$$ in the stack of coherent sheaves of rank $$1$$ and degree $$d$$ with determinant $$L$$?

• Just curious- why did you take Yellow Pig as a name. What does that have to do with mathematics. – aginensky Aug 11 at 15:54
• – Yellow Pig Aug 13 at 6:01