Timeline for Example of non-holonomic D-module and explicit computation of characteristic variety
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 16, 2017 at 14:03 | vote | accept | C. Dubussy | ||
| Jan 16, 2017 at 12:57 | answer | added | Ketil Tveiten | timeline score: 9 | |
| Jan 16, 2017 at 12:44 | comment | added | C. Dubussy | Oh yes, sorry, you're right. It is difficult to precise how complex must be the system, but perhaps it would be very helpful to compute the characteristic variety of something like $$\{f(z,w)\partial_z + g(z,w)\partial_w + h(z,w), f'(z,w)\partial_z + g'(z,w)\partial_w + h'(z,w)\}$$ with $f,g,h,f',g',h'$ polynomials of low degree.Of course some of these polynomials can be constant but not all, if possible. | |
| Jan 16, 2017 at 12:38 | comment | added | Simon Wadsley | Can you be more precise about how non-trivial? With regards the inequality, it goes the other way. The dimension of the characteristic variety is at least dim $X$ not at most. | |
| Jan 16, 2017 at 12:31 | comment | added | C. Dubussy | Mmm, yes I would prefer less trivial examples. But, I have nonetheless a question. How could $\text{char}(D_X/D_X Q)$ be $T^*X$ since we know in general that $\text{dim}\text{char}(A) \leq \text{dim} X.$ ? | |
| Jan 16, 2017 at 12:16 | comment | added | Simon Wadsley | If you choose coordinates $z_1,z_2$ for $\mathbb{C}^2$ then $Q=0$ and $P=\{\mathrm{d/d}z_1,\mathrm{d/d}z_2\}$ seem to satisfy your requirements. Then $\mathrm{char}(D_X/D_XP)$ is just the zero section of $T^\ast X$ and $\mathrm{char}(D_X/D_XQ)$ is the whole of $T^\ast X$. Do you want to apply further constraints or do these satisfy your requirements? | |
| Jan 16, 2017 at 9:54 | history | asked | C. Dubussy | CC BY-SA 3.0 |