Timeline for How can I construct D-modules over projective space using explicit differential equations?

9 events

when toggle format	what		by	license	comment
Jan 17, 2017 at 21:20	vote	accept	54321user
Jan 17, 2017 at 15:30	comment	added	Avi Steiner		Also take a look at "D-modules on Smooth Toric Varieties" (arxiv.org/abs/math/0007099)
Jan 3, 2017 at 15:49	vote	accept	54321user
Jan 3, 2017 at 15:49
Jan 3, 2017 at 15:49	vote	accept	54321user
Jan 3, 2017 at 15:49
Jan 3, 2017 at 13:33	comment	added	Ben Webster♦		Look at Section 11.3 of Hotta, Takeuchi and Tanisaki (math.columbia.edu/~scautis/dmodules/hottaetal.pdf). The essential point is that these vector fields (thought of as functions on $T^\mathbb{P}^n$) generate all the polynomial functions on the cotangent bundle, since the induced map from $T^\mathbb{P}^n$ to $(n+1)\times (n+1)$-matrices is a resolution of singularities of the rank $\leq 1$ matrices.
Jan 3, 2017 at 4:38	comment	added	54321user		Oh, why is that true? Do you have a reference?
Jan 3, 2017 at 2:24	comment	added	Ben Webster♦		@user251222 Those expressions don't even make sense as differential operators, since they have poles at $\infty$. The polynomial differential operators are generated by $x_i\frac{\partial}{\partial x_j}$.
Jan 3, 2017 at 1:42	comment	added	54321user		Will $\mathcal{D}_{\mathbb{P}^n}(\mathbb{P}^n) = \mathbb{C}\left[\frac{\partial}{\partial x_0}, \ldots, \frac{\partial}{\partial x_n}\right]$?
Jan 3, 2017 at 0:58	history	answered	Ben Webster♦	CC BY-SA 3.0