Mathematics Seminar
Date: Wednesday, 25 September 2024
Time: 3:30 PM
Venue: Seminar Hall
Generalizing Gurjar's Hyperplane section theorem
Mohit Upmanyu
Chennai Mathematical Institute.
25-09-24

---

Abstract

In this talk, We introduce the notion of an AmAC, and prove some of their basic properties. we then the use these prove the following theorem:

Let $K$ be an uncountable algebraically closed field, Let $X$ be an irreducible subvariety of $Spec(K[[x_1,...,x_n]])$. Suppose there exist an sequence of hyperplanes $H_i$, such that the singular locus of $X \cap H_i$ has dimension $d$ and the multiplicity of the singular locus of $X \cap H_i$ tends to infinity as $i$ tends to infinity. Then there exists a hyperplane $H$, such that the singular locus of $X \cap H$ has dimension \geq $d+1$