All Questions

Let $f: X \to S$ be a morphism of locally ringed spaces and $\triangle: X \to X \times_S X$ the corresponding diagonal morphism with kernel sheaf $\mathcal{I} = \ker \triangle^{\flat}$. Definition: ...

Let $V$ be a complex vector space. Consider the algebra $D(\mathbb{P}(V),\mathcal{O}(n)))$ of global differential operators from line bundle $\mathcal{O}(n)$ to itself, here $n \in \mathbb{Z}_{\...

I have heard that there is the following abstract definition due to Grothendieck of differential operators on a module $M$ over a commutative associative unital algebra $A$ over a field of ...

Let $p\colon \mathbb{R}^2 \to \mathbb{R}$ be a polynomial with a non-vanishing gradient at $p^{-1}(0)$. Then, the implicit function theorem says that $S = \{(x,y) \in \mathbb{R}^2 \mid p(x,y) = 0\}$ ...

In Bjork, Analytic D-modules and applications, the following definition of a Fuchsian operator is given: Here, I believe, $D(0)=\mathcal{O}$, the zeroth filtered piece of the ring of germs of ...