A polynomial vector field on a complex plane C^2 defines a foliation of the plane and one would like to know when the leaves of this foliation are algebraic, i.e. when the analytic integral curves are algebraic. This is a hard unsolved problem. I will suggest a conjectural approach to this problem which uses the reduction of the vector field modulo primes p. It turns out that the corresponding problem in characteristic p is easy to solve. We then conjecture that the original vector field is algebraic if and only if its reduction modulo a prime p is algebraic for almost all p. We have some partial results towards proving this conjecture. This is a work in progress with D. Leshchiner.


https://zoom.us/join
Meeting ID: 908 611 6889
Passcode: 362880

Subscribing the Mathematics Colloquium mailing list:
https://groups.google.com/g/ipm-math-colloquium