Bertini's theorem over finite field and Frobenius nonclassical varieties
报告题目：Bertini's theorem over finite field and Frobenius nonclassical varieties
报告专家：段炼（上海科技大学）
报告时间：2023年6月27日，14:30-15:20，
报告地点：数学学院东409
报告摘要：Bertini's theorem is a fundamental algebraic geometrical result in characteristic zero. However, in positive characteristic, especially over a finite field, there are counterexamples. An approach to remedy this situation could be to keep extending the ground field until the transitivity is recovered. In this talk, we will discuss the effective lower bound (with respect to certain geometric properties of the variety) of the ground field over which there is at least one transverse subspace to the given variety. The sharpness of our result is related to the Frobenius nonclassical type varieties. Their geometric properties will also be discussed if time allows. This is a joint work with Shamil Asgarli and Kuan-Wen Lai.
邀请人：许宾