动力系统讨论班——A regularization theorem for bounded-degree self-maps

报告人：杨舍(北京大学)

时 间：2024年5月16日（星期四），下午4:00-5:00

地 点：海纳苑2幢102

摘 要：We prove that over an algebraically closed field of arbitrary characteristic, a bounded-degree self-map of an irreducible projective variety can be regularized. That is to say, there exists another projective variety birational to the original one such that the bounded-degree self-map becomes an automorphism after birational transformation. Over the field of complex numbers, this result was stated in an article by S. Cantat and the proof backs to a work of A. Huckleberry and D. Zaitsev. The original proof is not purely algebraic. Inheriting their methods, we give a purely algebraic proof of this statement in arbitrary characteristic. If time permits, we will also discuss an application of this result towards the dynamical Mordell-Lang problem in positive characteristic.

联系人：叶和溪（yehexi@zju.edu.cn)