A stacky approach to linearisation of non-resonant vector fields

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，贾甲

Speaker：

Bongiorno Federico (YMSC)

Time：

Fri., 15:30-16:30, Dec. 13, 2024

Venue：

B725, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Title：

A stacky approach to linearisation of non-resonant vector fields

Abstract：

Whilst studying differential equations, Henri Poincar\'{e} showed that, given any non-resonant vector field $\partial$, there exists a formal change of coordinates such that $\partial$ can be locally expressed in a particularly simple linear form $\sum_i c_i \, x_i \partial / \partial x_i$, for some scalars $c_i$. By employing a stack-theoretic approach, together with some deformation theory, we reprove the above theorem in a purely algebraic context, extending the result to singular varieties.