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.
